The Shedd Aquarium, the
Field Museum of Natural History, and the
Museum of Science and Industry are all good suggestions. They are all first-rate.
If you're into more "touristy" things, head down to Navy Pier, which is actually the pier of the old Naval station converted into something of a small amusement park. Lots of food places, many seafood, all of them very good, but my favorite is
Bubba Gump Shrimp Co. Other possibilities include touring the harbor on a boat, or doing one of the many river tours. My favorite of those is the
Architecture River Cruise. Chicago is known for its architectural diversity, and the tour is both informative and a relaxing way to spend an afternoon.
At night, go down to State Street. It is brightly lit, people (and police) are everywhere, so it's perfectly safe, and basically everything open is a bar, restaurant, or nightclub with live music. Menus are posted on the windows, so pick one with food you like and go in. It is almost impossible to be disappointed because the competition is just too high; places that aren't awesome simply do not last.