Make a name for yourself in a smaller town and build a respected portfolio and base of clients (not just web-based companies). I’d suggest going the entrepreneurial route at first and getting your work through freelance (preferably after working for a small business that would enable you to efficiently network and acquire contacts).
Only then may you even have a shot at getting a job in New York. Unfortunately you need a lot more than talent and skill to get hired there (at least in any place worth-while). You need to have names to drop, a notable client history, a history of hitting dead-lines with optimum customer satisfaction, and a killer unique portfolio that will separate you from the crowd.
The fact that you have to post on this forum concerning “graphic design”, a heavily competitive field in NYC, shows that you are not ready to be working in the city. If you don’t already know the major players and have personal connections that will impress people looking at your resume, you don’t have much of a chance at landing anything that will keep you fed and housed. Sure you can find a job (eventually), but that doesn’t mean it will sustain your living in such an expensive city.
However, it’d be super cool if I’m wrong. There’s a possibility you’ll get a cheap enough place, and a so-so graphic design job that will pay just enough for you to grow your career from within New York. Immediacy is always nice, although you’ll also be directly faced with competition for the best local clients.