All the Manhattan schools have fully furnished subsidized housing to decrease prices for their students. That means MSSM, NYU, Columbia and Cornell.
NYU and Columbia are regular dorm hall setups (communal bathrooms, blech!). MSSM is apartment style with 4/6 person suites and two people per bathroom. MSSM's housing is the best I saw in NYC, hands down blowing away NYU and Columbia. I still have nightmares about the night I spent in Bard Hall *shudder*. Can't comment on Cornell's housing, though, as I didn't apply there.