Buddy Guys is great (you can check for acts online), I can recommend the Chicken Fried Steak with Collared Greens and Garlic Mash - it's just around the corner from the Chicago Hilton and Towers.
I went to the Aquarium, which was fantastic, but it was a long, long wait in the queue, which isn't pleasant if it's cold / windy.
If you travel outside the city, then the Hala Kahiki is well worth a visit - Tropical drinks in one of the few original Tiki Bars still operating outside of the West Coast.
Enjoyed going to Wrigley Field, it's worth going even if it's closed, just for the architecture - there's a street nearby that has a preservation order on it, on which every house has a different style windows / doors etc, which doesn't sound as impressive as it really is...
The Water Pumping station is worth a look in (one of the few buildings to survive the great Chicago fire) and it's within walking distance of the Chicago Museum of Modern Art.