if you apply to the more expensive schools you might get lucky with a scholorship. i get 7,500 a year from northeastern (boston), so that's why i'm here now. it's still very expensive, but i manage to swing it with a perkins grant, fed stafford and private loans. i thought about going to school in NYC, but it was too close to home at the time (new jersey). as boston goes, it's pretty much the same cost of living in new york, maybe higher. apartments in the nu area are pretty expensive, unless you go out to mission hill, brighton, allston, jp, somerville, ect. in fenway, kenmore, back bay think 1300+ for a 2br, and not even a nice one. the city is cool though, but its small compared to nyc. everything closes early (2am), which is ******* lame. overall i like it though. you really need to explore the area to fully appreciate it. and there are a ton of schools here.
sometimes its worth it to live in the slightly more expensive city just for the experience of living there. just figure out how to save hardcore and do as much on the cheap as possible. but it really depends on your situation.