There are many ideas suggested in this thread a few years back. http://discuss.amtraktrains.com/index.php?/topic/31542-chicago-union-station-layover/ There is also the Clinton Blue Line 'L' station 2 blocks south and the Quincy Brown/Orange/Pink Lines station 3 blocks to the east. Lots of places you can get to on the 'L' for a $2.25 flat fare.
If you have a sleeper, you can use the wonderful Metropolitan Lounge to store your luggage while exploring the city. If in coach, there are some lockers (reasonably priced, IIRC) near the baggage claim section of the station.
Thanks. We have come into Chicago on a train before but not really to sightsee. First time in a roomette with a tiny toilet. That is going to be weird.