Going to be in Chicago the entire week June 28th - July 1st for work. I'm going to stay the weekend and bring my bike. I've never been to the city when it's above... 15 degrees or so. So I really look forward to riding in some traffic, seeing the waterfront, and sweating my ass off.
You could check the chainlink (a cycling specific chicago social networking site) calender. There are usually a few things going on. Right now there is a night architecture tour of the loop and a frozen dessert ride. you could check to see if anything else pops up. Otherwise just get a map and ride around. I prefer the loop and the north, north/west parts of the city, the lakefront trail is nice but I tend to get bored quickly if I don't have to focus on riding all of the time.