Craigslist.

Just make sure you don't fork money over to someone before you get to the city and have a chance to see the apartment/room, check the person out, etc. Lots of people get scammed that way.

Also, if you're just looking for a city with a decent transit system where you can take classes (and if the sentimental reason for NYC isn't that overwhelming), you can do that anywhere, and for a lot cheaper. Chicago might work - and the housing situation is way easier to deal with, and far less expensive.