A few quick thoughts:
-stay downtown (between both campuses)
-if budget is an issue: Priceline!
-CTA red line runs to Northwestern
-no CTA trains (only bus) to U. of C., but you can take Metra Electric

Edited to note that the CTA green line does run to U of C as posted below. Oops. I guess it's just my own experience that I never took it when I lived in Hyde Park as a kid...