Our national championship (for acrobatic gymnastics) was in Louisville last year—at the same venue even. I didn't have much free time since we were at the training center with athletes in nearly every rotation, but downtown Louisville had some fun things to do. The convention center is close to 4th street, which has a lot of restaurants and live music most nights. They have a charming arts district a few minutes from downtown and there's always the more "touristy" attractions such as Churchill Downs, the Jack Daniels Distillery and the Louisville Slugger Factory, all of which have tours.
We stayed at a hotel within walking distance of the convention center—it made it very convenient to go back and forth from the competition—which I highly recommend because parking downtown is a nightmare and expensive.