If you're looking for a show to see this weekend, perhaps something with a good amount of humor in it, you might want to take a look at Too Much Light Makes The Baby Go Blind
. Yes, it's a mouthfull, but I've been attending this show for several years now (it changes every week). It's on the corner of Foster and Ashland on the northside, near the lake. If you plan on showing up either Friday or Saturday night, get there early as they tend to sell out.
If you feel like wasting an entire day riding roller coasters, you can go to SIx Flags Great America up in Gurnee, IL. It's about a half hour drive north of the Hyatt.
We also have the following museums: Field Museum, Shed Aquarium, Adler Planetarium, Museum of Science and Industry, Art Institute of Chicago and a few smaller ones that I don't know very well.
If you're looking for something in particular, let me know and I'll see if I can think of something.