Fair enough, living in Manhattan is not cheap, though it does come with extra benefits. Nevertheless, there are a few things to keep in mind:
1. Subsidized housing is available to first years.
2. The stipend has a 9-month duration. So, there is some additional summer funding available at NYU, or you could (say) get a paid internship elsewhere during the summer.
3. You can pay very reasonable rents by living in Brooklyn, Roosevelt Island, Jersey City, etc. Then there are the perennial favorites such as taking multiple roommates, etc.
Now, if you live alone in Manhattan, take the taxi everywhere, and eat out every night, that's a different story .