Some people claim New York City as the capital of the world. I don't dispute its importance in global affairs or its role in business and trade. But New York is an American city: it's a place where you can find just about every shade of humanity, and through its diversity of individual and family, a whole unlike any other in the world (save, perhaps, London).
I spent a summer in New York working for a big investment bank (every day of the summer, not surprisingly), and with cousins, friends, and now a sibling living there, have visited many many times.
As much as I like the city, there's a lot more to the state. One of the best spots is way up north in Ithaca, where geologics have left us with some phenomenal natural diving boards. Just be careful if you visit the gorges, as some are incredibly slippery!