Neither route is going to be pretty, but you should probably take 90 (Kennedy Expy). However, don't take it all the way to 290 (Eisenhower Expy). Rather, exit at Ogden Avenue, and follow this "angle" street southwesterly to the UC from 90.

Another option may be to take the El (Blue Line) from O'hare to the Loop (~45 Minutes). Then rent a car from a city location, if you really need one. Else, short cab to the UC from the El stop.