If you're at the convention center, your best bet might be to check out the museums on the museum campus (natural history, aquarium, planetarium in most-to-least order of my preference), or walk around Chinatown.
If you're downtown it's worth walking around the lakefront, whether it's Millennium Park or just along the lake if the weather's nice. I recommend peeking into the Chicago Cultural Center across the street from the bean, formerly the home of the Chicago Public Library, which has beautiful mosaics and stained glass, including a Tiffany glass dome.
The Newberry Library north of downtown is nice, and there's usually something strange going on in the park in front of the library, plus the Gold Coast has some amazing historic homes.
Have fun! If you go to the Lincoln Park Zoo let me know how the polar bear enclosure is coming along! :D