In terms of suburbs, Evanson is very cool -- it's pretty city-like and has many beautiful homes. It tends to be on the expensive side -- if you're looking for an inexpensive apartment, check out Rogers Park, which is the Chicago neighborhood just south of Evanston. I'd try to stay on the eastern end of either Evanston or Rogers Park.
Check out the
Chicago Reader Spacefinder which is the best way to find an apartment in the area.