Even if you only have a day, you can hit a number of attractions that are in close proximity to each other. If you go downtown Lakeshore Drive, you can hit the Field Museum, Shedd Aquarium, and Adler Planetarium within walking distance of each other. You can then stroll along the beach, take a dip in the frigid waters of Lake Michigan, or walk and enjoy the skyline of Chicago. If the beach isn't your thing, then you can take a walk in Grant Park. If you're willing to walk far enough, you can check out Lincoln Park Zoo.
If walking's not your thing, then the bus system is pretty easy to navigate and prompt. I do not recommend driving, unless you're willing to pony up for parking or willing to drive around looking for a coveted parking spot. Either way, you may still have a considerable walk to get to where you want to be.
From that spot there's plenty to do at night, and Buddy Guy's Legends isn't that far away. If you wanna do the Blues thing, I suggest hitting up North Halsted to be able to hit a few famous clubs, in a close proximity. B.L.U.E.S. is a cozy little club with legendary acts in the crowd and stage. Kingston Mines is also on the same street - bigger club but same legendary status. Rosa's is about 4 miles from this area, but another great Blues club. Blue Chicago is also a few miles away.