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.
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.
The Impressionists show the typical pattern: they were born all over France (Pissarro was born in the Carribbean) and died all over France, but what defined them were the years they spent together in Paris.