Great cities attract ambitious people. You can sense it when you walk around one. In a hundred subtle ways, the city sends you a message: you could do more; you should try harder.
The surprising thing is how different these messages can be. New York tells you, above all: you should make more money. There are other messages too, of course. You should be hipper. You should be better looking. But the clearest message is that you should be richer.
What I like about Boston (or rather Cambridge) is that the message there is: you should be smarter. You really should get around to reading all those books you've been meaning to.
When you ask what message a city sends, you sometimes get surprising answers. As much as they respect brains in Silicon Valley, the message the Valley sends is: you should be more powerful.
That's not quite the same message New York sends. Power matters in New York too of course, but New York is pretty impressed by a billion dollars even if you merely inherited it. In Silicon Valley no one would care except a few real estate agents. What matters in Silicon Valley is how much effect you have on the world. The reason people there care about Larry and Sergey is not their wealth but the fact that they control Google, which affects practically everyone.
How much does it matter what message a city sends? Empirically, the answer seems to be: a lot. You might think that if you had enough strength of mind to do great things, you'd be able to transcend your environment. Where you live should make at most a couple percent difference. But if you look at the historical evidence, it seems to matter more than that. Most people who did great things were clumped together in a few places where that sort of thing was done at the time.
You can see how powerful cities are from something I wrote about earlier: the case of the Milanese Leonardo. Practically every fifteenth century Italian painter you've heard of was from Florence, even though Milan was just as big. People in Florence weren't genetically different, so you have to assume there was someone born in Milan with as much natural ability as Leonardo. What happened to him?
If even someone with the same natural ability as Leonardo couldn't beat the force of environment, do you suppose you can?
I don't. I'm fairly stubborn, but I wouldn't try to fight this force. I'd rather use it. So I've thought a lot about where to live.
I'd always imagined Berkeley would be the ideal place—that it would basically be Cambridge with good weather. But when I finally tried living there a couple years ago, it turned out not to be. The message Berkeley sends is: you should live better. Life in Berkeley is very civilized. It's probably the place in America where someone from Northern Europe would feel most at home. But it's not humming with ambition.
In retrospect it shouldn't have been surprising that a place so pleasant would attract people interested above all in quality of life. Cambridge with good weather, it turns out, is not Cambridge. The people you find in Cambridge are not there by accident. You have to make sacrifices to live there. It's expensive and somewhat grubby, and the weather's often bad. So the kind of people you find in Cambridge are the kind of people who want to live where the smartest people are, even if that means living in an expensive, grubby place with bad weather.
As of this writing, Cambridge seems to be the intellectual capital of the world. I realize that seems a preposterous claim. What makes it true is that it's more preposterous to claim about anywhere else. American universities currently seem to be the best, judging from the flow of ambitious students. And what US city has a stronger claim? New York? A fair number of smart people, but diluted by a much larger number of neanderthals in suits. The Bay Area has a lot of smart people too, but again, diluted; there are two great universities, but they're far apart. Harvard and MIT are practically adjacent by West Coast standards, and they're surrounded by about 20 other colleges and universities. 
Cambridge as a result feels like a town whose main industry is ideas, while New York's is finance and Silicon Valley's is startups.
When you talk about cities in the sense we are, what you're really talking about is collections of people. For a long time cities were the only large collections of people, so you could use the two ideas interchangeably. But we can see how much things are changing from the examples I've mentioned. New York is a classic great city. But Cambridge is just part of a city, and Silicon Valley is not even that. (San Jose is not, as it sometimes claims, the capital of Silicon Valley. It's just 178 square miles at one end of it.)
Maybe the Internet will change things further. Maybe one day the most important community you belong to will be a virtual one, and it won't matter where you live physically. But I wouldn't bet on it. The physical world is very high bandwidth, and some of the ways cities send you messages are quite subtle.
One of the exhilarating things about coming back to Cambridge every spring is walking through the streets at dusk, when you can see into the houses. When you walk through Palo Alto in the evening, you see nothing but the blue glow of TVs. In Cambridge you see shelves full of promising-looking books. Palo Alto was probably much like Cambridge in 1960, but you'd never guess now that there was a university nearby. Now it's just one of the richer neighborhoods in Silicon Valley. 
A city speaks to you mostly by accident—in things you see through windows, in conversations you overhear. It's not something you have to seek out, but something you can't turn off. One of the occupational hazards of living in Cambridge is overhearing the conversations of people who use interrogative intonation in declarative sentences. But on average I'll take Cambridge conversations over New York or Silicon Valley ones.
A friend who moved to Silicon Valley in the late 90s said the worst thing about living there was the low quality of the eavesdropping. At the time I thought she was being deliberately eccentric. Sure, it can be interesting to eavesdrop on people, but is good quality eavesdropping so important that it would affect where you chose to live? Now I understand what she meant. The conversations you overhear tell you what sort of people you're among.
No matter how determined you are, it's hard not to be influenced by the people around you. It's not so much that you do whatever a city expects of you, but that you get discouraged when no one around you cares about the same things you do.
There's an imbalance between encouragement and discouragement like that between gaining and losing money. Most people overvalue negative amounts of money: they'll work much harder to avoid losing a dollar than to gain one. Similarly, though there are plenty of people strong enough to resist doing something just because that's what one is supposed to do where they happen to be, there are few strong enough to keep working on something no one around them cares about.
Because ambitions are to some extent incompatible and admiration is a zero-sum game, each city tends to focus on one type of ambition. The reason Cambridge is the intellectual capital is not just that there's a concentration of smart people there, but that there's nothing else people there care about more. Professors in New York and the Bay area are second class citizens—till they start hedge funds or startups respectively.
This suggests an answer to a question people in New York have wondered about since the Bubble: whether New York could grow into a startup hub to rival Silicon Valley. One reason that's unlikely is that someone starting a startup in New York would feel like a second class citizen.  There's already something else people in New York admire more.
In the long term, that could be a bad thing for New York. The power of an important new technology does eventually convert to money. So by caring more about money and less about power than Silicon Valley, New York is recognizing the same thing, but slower.  And in fact it has been losing to Silicon Valley at its own game: the ratio of New York to California residents in the Forbes 400 has decreased from 1.45 (81:56) when the list was first published in 1982 to .83 (73:88) in 2007.
Not all cities send a message. Only those that are centers for some type of ambition do. And it can be hard to tell exactly what message a city sends without living there. I understand the messages of New York, Cambridge, and Silicon Valley because I've lived for several years in each of them. DC and LA seem to send messages too, but I haven't spent long enough in either to say for sure what they are.
The big thing in LA seems to be fame. There's an A List of people who are most in demand right now, and what's most admired is to be on it, or friends with those who are. Beneath that the message is much like New York's, though perhaps with more emphasis on physical attractiveness.
In DC the message seems to be that the most important thing is who you know. You want to be an insider. In practice this seems to work much as in LA. There's an A List and you want to be on it or close to those who are. The only difference is how the A List is selected. And even that is not that different.
At the moment, San Francisco's message seems to be the same as Berkeley's: you should live better. But this will change if enough startups choose SF over the Valley. During the Bubble that was a predictor of failure—a self-indulgent choice, like buying expensive office furniture. Even now I'm suspicious when startups choose SF. But if enough good ones do, it stops being a self-indulgent choice, because the center of gravity of Silicon Valley will shift there.
I haven't found anything like Cambridge for intellectual ambition. Oxford and Cambridge (England) feel like Ithaca or Hanover: the message is there, but not as strong.
Paris was once a great intellectual center. If you went there in 1300, it might have sent the message Cambridge does now. But I tried living there for a bit last year, and the ambitions of the inhabitants are not intellectual ones. The message Paris sends now is: do things with style. I liked that, actually. Paris is the only city I've lived in where people genuinely cared about art. In America only a few rich people buy original art, and even the more sophisticated ones rarely get past judging it by the brand name of the artist. But looking through windows at dusk in Paris you can see that people there actually care what paintings look like. Visually, Paris has the best eavesdropping I know. 
There's one more message I've heard from cities: in London you can still (barely) hear the message that one should be more aristocratic. If you listen for it you can also hear it in Paris, New York, and Boston. But this message is everywhere very faint. It would have been strong 100 years ago, but now I probably wouldn't have picked it up at all if I hadn't deliberately tuned in to that wavelength to see if there was any signal left.
So far the complete list of messages I've picked up from cities is: wealth, style, hipness, physical attractiveness, fame, political power, economic power, intelligence, social class, and quality of life.
My immediate reaction to this list is that it makes me slightly queasy. I'd always considered ambition a good thing, but I realize now that was because I'd always implicitly understood it to mean ambition in the areas I cared about. When you list everything ambitious people are ambitious about, it's not so pretty.
On closer examination I see a couple things on the list that are surprising in the light of history. For example, physical attractiveness wouldn't have been there 100 years ago (though it might have been 2400 years ago). It has always mattered for women, but in the late twentieth century it seems to have started to matter for men as well. I'm not sure why—probably some combination of the increasing power of women, the increasing influence of actors as models, and the fact that so many people work in offices now: you can't show off by wearing clothes too fancy to wear in a factory, so you have to show off with your body instead.
Hipness is another thing you wouldn't have seen on the list 100 years ago. Or wouldn't you? What it means is to know what's what. So maybe it has simply replaced the component of social class that consisted of being "au fait." That could explain why hipness seems particularly admired in London: it's version 2 of the traditional English delight in obscure codes that only insiders understand.
Economic power would have been on the list 100 years ago, but what we mean by it is changing. It used to mean the control of vast human and material resources. But increasingly it means the ability to direct the course of technology, and some of the people in a position to do that are not even rich—leaders of important open source projects, for example. The Captains of Industry of times past had laboratories full of clever people cooking up new technologies for them. The new breed are themselves those people.
As this force gets more attention, another is dropping off the list: social class. I think the two changes are related. Economic power, wealth, and social class are just names for the same thing at different stages in its life: economic power converts to wealth, and wealth to social class. So the focus of admiration is simply shifting upstream.
Does anyone who wants to do great work have to live in a great city? No; all great cities inspire some sort of ambition, but they aren't the only places that do. For some kinds of work, all you need is a handful of talented colleagues.
What cities provide is an audience, and a funnel for peers. These aren't so critical in something like math or physics, where no audience matters except your peers, and judging ability is sufficiently straightforward that hiring and admissions committees can do it reliably. In a field like math or physics all you need is a department with the right colleagues in it. It could be anywhere—in Los Alamos, New Mexico, for example.
It's in fields like the arts or writing or technology that the larger environment matters. In these the best practitioners aren't conveniently collected in a few top university departments and research labs—partly because talent is harder to judge, and partly because people pay for these things, so one doesn't need to rely on teaching or research funding to support oneself. It's in these more chaotic fields that it helps most to be in a great city: you need the encouragement of feeling that people around you care about the kind of work you do, and since you have to find peers for yourself, you need the much larger intake mechanism of a great city.
You don't have to live in a great city your whole life to benefit from it. The critical years seem to be the early and middle ones of your career. Clearly you don't have to grow up in a great city. Nor does it seem to matter if you go to college in one. To most college students a world of a few thousand people seems big enough. Plus in college you don't yet have to face the hardest kind of work—discovering new problems to solve.
It's when you move on to the next and much harder step that it helps most to be in a place where you can find peers and encouragement. You seem to be able to leave, if you want, once you've found both. The Impressionists show the typical pattern: they were born all over France (p*ssarro was born in the Carribbean) and died all over France, but what defined them were the years they spent together in Paris.
Unless you're sure what you want to do and where the leading center for it is, your best bet is probably to try living in several places when you're young. You can never tell what message a city sends till you live there, or even whether it still sends one. Often your information will be wrong: I tried living in Florence when I was 25, thinking it would be an art center, but it turned out I was 450 years too late.
Even when a city is still a live center of ambition, you won't know for sure whether its message will resonate with you till you hear it. When I moved to New York, I was very excited at first. It's an exciting place. So it took me quite a while to realize I just wasn't like the people there. I kept searching for the Cambridge of New York. It turned out it was way, way uptown: an hour uptown by air.
Some people know at 16 what sort of work they're going to do, but in most ambitious kids, ambition seems to precede anything specific to be ambitious about. They know they want to do something great. They just haven't decided yet whether they're going to be a rock star or a brain surgeon. There's nothing wrong with that. But it means if you have this most common type of ambition, you'll probably have to figure out where to live by trial and error. You'll probably have to find the city where you feel at home to know what sort of ambition you have.