Copying some stuff by various posters from other threads (because indeed we are all studying):
Housing is great, but you shouldn't forget to 1) be specific about what you'd like, but at the same time (prioritize). If you say you want something under $1500, but you need a 2 BR on the corner of broadway with a dishwasher and a spacious kitchen, you'll get maybe one of those things. So list your important stuff. I said I wanted the cheapest possible 2 BR and if it couldn't be under $1500, the largest 1 BR that I could get for that. I was really happy, and I'm extremely close to the law school (though everyone is also pretty close). My living situation is pretty common except for other couples seem to have nicer apartments that cost more. If cheap is your biggest priority, make that clear!
It costs between $725 and $1100 per month for your own bedroom in a shared 2, 3 or 4 bedroom apartment.
The vast majority of CLS students live with other law students. Some live in singles or couples housing. A small minority lives with non-law grad students (and only because they requested it.) Theoretically it's possible to live in undergrad dorms, I think, but you'd have to specifically ask for it.
And some pictures someone made.
http://www1.cs.columbia.edu/~senrique/p ... apartment/
There are some singles and couples apartments, but they are scarce, and most people don't get them (unless they are, in fact, part of a couple). (And if they do get them, they're usually a bit further from the school, though still not really far.) Lenfest is supposed to be better quality than the other apartment housing (better furniture, larger rooms), but it's also several hundreds of dollars more expensive. Some who live there say it's worth it to them, others who live there say that in hindsight they wouldn't have minded sharing an apartment and saving the money.
If you search for "Lenfest" on this board, you'll probably find more info.