You can certainly fill 7 days in Chicago, as long as you don't expect to do Blockbuster things every single day. Look at a few things beyond the core of the downtown area. Skipping the obvious big museums, a few other things come to mind immediately:
Graceland cemetary is wonderful and ofter overlooked, distinctive graves of many famous people, many of them reflecting their specialities (Sullivan's, for example, is a bandbox of a perfect little Sullivan building).
Get a car, drive up to the Bahai temple and then on to Milwaukee to see the fantastic art museum and to tour the Pabst mansion if you're interested in architecture. If you want some cheap shopping, there is an outlet mall right on the highway just inside Wisconsin.
Take a couple easy days during the daytime and see some shows - Chicago has fabulous theater. Ditto for the symphony and opera (if they're in season in May).
Go to the architecture foundation on S. Michigan and sign up for a couple tours, they have some nice walking tours, and their boat trip on the river is a must do.
Take in a baseball game at Wrigley (while it still IS Wrigley). Lest I get a raspberry from my southside friends, you CAN also go to a Sox game, but if I were to choose one for a visitor, Wrigley is still the ultimate historical ballpark.
Walk up the lakefront and then back to your hotel through the city streets. Depending on how much you want to walk, you can start out from Oak Street and walk to North Avenue, to Fullerton, to Belmont or to Irving Park - each major street here is about a mile. And then cut over and walk back down Broadway/Clark. Lot's of interesting shops and restaurants.
Eat yourself silly and collapse into a coma in your hotel room.
Explore our ethnic restaurants, many of which are easily reachable even without a car, for example, the Red Line will take you north to Devon - home of Indian/Pakistani food, to Arglye the northside asian area - or south to Chinatown, which can be easily reached from the Cermak/Chinatown stop.
Go to Hyde Park and visit the Museum of Science and Industry and then explore the University of Chicago campus. Not terribly convenient from the L, but several bus lines will take you right there.
I also noticed recently that the historic Chicago Theater (on State St.) does facility tours, and that could be fun.
May is a little early, but check out if there are any concerts in Millennium Park. Get a picnic and sit on the grass.