Absolutely. I wouldn't go for student housing at NYU...it just doesn't seem worth it, especially when there are so many good options a very short subway ride away. It's just a matter of doing the research on various neighborhoods, etc. Another way to use Craigslist is to search the "rooms/shared" section, and in the search field type "grad student" or "law student" or something. You'll find other people like you with rooms to rent, etc. The obvious disadvantage to off-campus over on-campus is that you'll have less time to make housing arrangements, but I think it's worth it.
There is another big disadvantage to living off-campus your first year, and that is the fact that 2/3 of the incoming students do live on-campus. I say that this is a big disadvantage because living off can (but of course, not assuredly will) result in you being outside of an opportunity to really get to know others. There are a lot of happenings going on locally, be they parties, trips to eat, bar hang-outs, colloquia, seminars, etc, that happen all of the time. The further away you are your first year, the harder it is to really get immersed. I think that the money difference is more than made up for by the social and other benefits that come from living with others going through the same experience.
Don't get me wrong, there can be some pitfalls to living in a res hall too, such as the inability to get away from some people, the stress during finals, etc, but overall I think living on is great for first year students.