ScottC: Looks like you'll only have about 6 hrs layover. If you like to arrive 2 hrs prior to departure of your outgoing flight then that leaves you only about 4 hrs. On a sunday afternoon, traffic to downtown chicago driving takes about 30 mins. If you take the "El" -- the elevated train, then you can reach downtown in about 40 mins.

Assuming the worst 1 hr each way, that leaves you with 2 hrs to spare once you reach downtown.

Here are my suggestions:

• From O'Hare, follow the signs labelled CTA or ask someone how to get to the "El" stop. Once there, take the Blue Line trains towards downtown (there are 2 lines, one labelled Forest Park, and the other labelled Cermak, it doesn't matter which one you get on).
• Get off at the Washington Ave or Jackson Ave stops.
• Follow the signs and transfer to the Red line trains going north (should be labelled Jarvis/Howard).
• Get off at Chicago Ave stop. Leave the station and walk onto the street.
• Walk 2 blocks east until you hit Michigan Ave. You will now be at the heart of the "Magnificent Mile/Water Tower Area". This is some of the best shopping in the city.
• To return to O'Hare, simply reverse the above directions.

My suggestions would be to visit the mall in the Water Tower place, there are plenty of electronic shops there. You will also be within a few blocks walking of the Hancock tower, Water tower, dozens of department stores. Shopping generally ends around 5-6 PM (CST). I lived in downtown Chicago for 2 years and loved it. Taking the trains to/from ORD is the best way to go, as unexpected traffic jams can occur even on the weekends.