hey. my friends who've attended nyu and not gotten subsidized on-campus housing have for the most part chosen to live in brooklyn, which is a short commute from nyu on the subway, or right off the path train in new jersey (hoboken, for example.) i had a friend who lived in harlem and would hop on the express a train to get downtown relatively quickly. these options will give you more bang/space for your buck in nyc since living downtown near campus tends to be very expensive. my suggestion would be for you to get in touch w grad students who are currently attending school there and get the lowdown. and, of course, to visit the campus and the aforementioned neighborhoods before you make a final decision. i personally would opt to live in brooklyn since that's where the action is these days anyway - but it depends on the kind of vibe/crowd you like.
congrats on your acceptance btw. nyc is a phenomenal city and you'll be the envy of the rest of the grad student population that is stuck in new haven, princeton, etc...