I have a friend that attends NYU Law and lives in on-campus graduate housing, and she pays a ton of money for an extremely small apartment with a roommate. The each have a room that is basically a glorified closet, and comes with a twin bed, a desk and some shelves- you really couldn't fit anything bigger in there. There's a small kitchen and no common area to speak of. It feels like a college dorm and not like a real apartment. If Wagner students are offered similar housing, I'd really encourage everyone to find housing not through NYU.
Greenwich Village is super expensive, but there are plenty of more affordable, wonderful places to live in NYC, especially if you consider the outer boroughs. I live in Astoria in Queens and I love it; there's a ton of young people here.