If you go to Northwestern, you can live pretty much anywhere off the red line (Howard/95th) and get to Northwestern in a reasonable amount of time (as long as the red line runs like it should, which, with the funding issues we have had lately, and the current construction is iffy). That's Lakeview, Wrigleyville, parts of Lincoln park, Andersonville, Rogers Park, and Uptown, as well as Chinatown and Bridgeport, just to name a few neighborhoods. You can also live off the Chicago, Division or North buses, which run fairly late (Division and North until approx. 1:30 am and Chicago 24hours), which opens up the near NW side to you. Wicker Park and the Ukrainian Village are really fun places to live, and you can get to Northwestern in about 25-30 minutes by public transit.
If you go to UChicago, you can live in Hyde Park.
I've lived in this city for five years, from north side to south side, and if it was me in that (wonderful!) conundrum, and I was picking a school purely on location, I'd pick Northwestern. Hyde park is a fun visit, but like others have said, it's an island.