Hey cutout,
When I worked at Columbia, plenty of the grad students/adjuncts would get either student housing or "off campus," i.e. not university sponsored-apartments in Washington Heights, in the immediate vicinity of the medical center on 168th Street, or in Hamilton Heights, around 145th Street heading toward the West Side. If you get a place near the medical center on 168, there's a free shuttle for students/staff that runs between there and the main campus at Morningside.
There is also a shuttle service to the Upper East Side (near Cornell and Rockefeller University), but I don't know if its open to Columbia students. Upper East Side isn't so fun, though.
I agree with Jed that the boroughs can be good, but I too commuted from Greenpoint to Columbia and it was more than I could take (I did the walk to Queens, then 7 to the A train), especially in the warm months.
If you are willing to travel a little bit for fun, then consider renting in Riverdale, in the Bronx. Its a really nice neighborhood, about 30 minutes to the campus. You can get a nice 1 bedroom in a great building for $1250 or so. Just know its not a terribly exciting place to live.