There is a Four Points right downtown (River North area) that's relatively new, if that's an option for you.
If you do the O'Hare option, you could have the shuttle bus take you to the Rosemont stop of the El, which would be less hassle than having to go to the airport. Transportation to O'Hare from Union is easier than Midway, as you can walk a couple blocks south and get the train at Canal street. For Midway, you'd have to transfer trains or take a bus or taxi.
Downtown is pretty even--may 10 minutes shorter in from Midway. There's more "stuff" around O'Hare--Midway is in a pretty industrial area. You could also get off the Blue Line El from O'Hare before you get to the loop and check out some of the neighborhoods, like Logan Square or Wicker Park/Bucktown.
I guess I'd vote O'Hare, in case you didn't figure that out!
"If you can't be a good example, then you'll have to be a horrible warning." Catherine Aird