In addition to the downtown area, we spent a little time in the Wrigleyville area (without getting to see Wrigley Stadium itself). It was a neat area also, not a grand as the downtown, but not ugly.
But we did not venture into the poorer neighborhoods or really to anywhere that I would call slums. We did drive by one area that is bad off on the way to the airport and saw lots of old houses that were boarded up. And the area around the airport is not pretty at all.
All in all it was a great trip and I looking forward to visiting again.