Paul Graham asks: "Could you reproduce Silicon Valley elsewhere, or is there something unique about it?." His answer: it's unique, but if you want to replicate it a few of the right people are all you need.
How would you recreate Manhattan? Like Silicon Valley, it's an enormously productive area despite a dearth of natural resources (besides access to water, which is not as valuable as it used to be). Most of the industries here rely on skilled, but not ridiculously skilled, labor (you couldn't have Silicon Valley without a few professors in the top .1% of their fields, but the media, finance, and law industries here can be quite successful without that kind of elite academic backing -- as long as the city still has a healthy fraction of the top 5% in each field).
What gives Manhattan its competitive advantage? The cost of living is so high that time is too valuable to waste.
Wasting someone's time is an easy way to impose a massive externality: if I interrupt a bond analyst or a tax attorney for a minute, I've spent a few dollars of someone's time at a lower cost to myself -- and it's unlikely that my interruption will provide that much gross benefit to either of us. But if I'm already paying for my time, I'm much less likely to waste it pestering people with a small probability of success -- it's a flat tax on sales spiels, sob stories, product pitches, and every other trick for converting a certain loss of time into a possible transfer of money.
Time here is valuable because real estate is valuable, and we're all forced to consume some real estate just to stick around. It's a virtuous cycle: people who can't afford the rent are priced out of the city, so the people who do live here are wealthier on average, so anyone who wants to spend time with wealthy people (e.g. someone in finance, law, or the media) has an incentive to move here, pushing prices up again for another round of the same.[1]
Three hundred years ago, geography made New Amsterdam a place worth living by bringing ships in; today, geography makes Manhattan worth the steep cost by keeping poor people out -- since we're on an island, sprawl goes from a continuum to a binary equation, lopping off most of left half of the net-worth bell curve.
It doesn't take an island to pull this off, though: if you really wanted to create another Manhattan (or an even Manhattanier Manhattan), all you recreate is the steep cost of showing up: a $5,000 annual fee for living in the city would suffice. Of course, no one will pay $5,000 to be the first person there, so you might require a few hundred highly skilled 'founders' to start the first couple hedge funds, law firms, and cable TV stations. Thereafter, the incentive structure is easy to understand: if you want to deal exclusively with very rich people with very valuable time, borrow whatever you can and move in (keeping in mind that valuable time for rich people means high wages for limo drivers, janitors, and assistants of all sorts). A few provisions for expelling people who commit crimes would also be helpful.
The most compelling part of this thought experiment is that the cost of an actual government would be absurdly cheap. If you made a Venn diagram of "People with access to $5,000," in one circle and "People who commit lots of crimes," in the other, the sliver of intersection would be the entire criminal population -- a police force about 10% as large as that of a no-fee city wouldn't be out of the question.
It's hard to imagine creating this in an existing city (expelling all the poor people wouldn't be good PR, even if what's left is an economic Garden of Eden), but one trick might be to do what Social Security did, and change the legal but not economic incidence of the tax; instead of charging people to be there, you'd just charge their employer (or school) to have them there. [2]
I'm not sure who would want to live in this kind of city, but a good way to guess would be to ask: who wouldn't be able to live there, and who would be happier without those people? Someone with lots of ideas and no plan for implementing any of them is out until the first success; this gives venture capitalists more time to focus on genuinely interesting plans. Aspiring writers with movie scripts and no movie experience can't afford the entry fee; film directors can use the hassle-free time as a dividend to work on more projects. Resident's won't participate in high total, low average class-action lawsuits, so the lawyers who create those won't prosper, while more productive ones (who craft low-dispute merger contracts and effective tax strategies) will. Depending on whether your taste in books leans more to Upton Sinclair or Ayn Rand, this is either hell or paradise -- a condition that's usually a good sign of an underexploited niche.
Most people probably agree that it's better to have Manhattan than to not have it, so I have to wonder -- why not create Manhattan, only more so?
[1] Indirectly, we spend more on real estate than the cost of our rent, because the square footage taken up by laundromats and restaurants and power plants also costs that much. If you want to figure out the difference, the best way would to to sum up all real estate value in New York, and find out how much it would cost to buy the same amount of land in, say, the middle of Kansas. That would get a rough estimate of how much people pay to price poor people out of New York.
[2] The effect is the same (whether I have to pay someone $105,000 so he'll willingly pay the $5K, or $100,000 plus $5K to the government, our balance sheets look the same), but the PR is much better.