An interesting day trip to neighborhoods. You can take any one of the 13 commuter trains outbound to a neighborhood or suburb of your choice, spend a few hours walking around, then reboard the train to the next stop.
Commuter Trains metrarail.com
metrarail.com/content/metra/en/home/maps_schedules/metra_system_map.html
CTA transitchicago.com
One interesting trip would be to take the METRA Electric southbound. You get to the train station from an entrance on Michigan Avenue - the station is below Millenium Park close to the Art Institute.
Click for a schedule
Steve Goodman : City Of New Orleanswww.youtube.com/watch?v=AJ0JgqoF2W4
You can ride the train south to the 59th St Station (5900 blocks south of downtown). When you get off you are in Hyde Park and the University of Chicago.
visit.uchicago.edu/explore.shtml
The Oriental Institute
1155 East 58th Street
Chicago, IL 60637
773-702-9514 - General Information
Directions to the Oriental Institute
Museum of Science and Industry
msichicago.org
Site of the 1893 World's Fair
Then you can head back to downtown, or continue south from either the 59th or 55th St Stations to Pullman. Pete Will tell us about Pullman
After Pullman you can return to the city, or continue south to the Blue Island. Change trains to the Rock Island Line and go north to 103rd St Station - go west to Longwood Drive and see the Irish Castle, then walk north along Longwood Drive looking at the impressive older homes. The train stops every 1/2 mile at 103rd, 107th, 111th. You can reboard the train at any station and return downtown.