There are several hotels within a short drive or walking distance from the stadium. They range from the modest (Hilton and that ilk) to more upscale (Crowne Plaza). Downtown there are many to choose from, but one that is rated one of the best in the USA is 21C.
If you do get a rental, it is a short drive (under 50 miles from downtown) to the bourbon trail south of Louisville in Bullitt county. On the way back you can visit Bernheim Forest and arboretum to complete a pleasant half-day outing.
Back in town, you should not miss taking an evening stroll across the Ohio river via the Big 4 bridge. It is a former railroad bridge that has been restored to a walking bridge by a joint effort of Kentucky and Indiana. The views are spectacular and there always seem to be many folks there, so you will not be worried about your personal safety.
The JB Speed art museum is undergoing a massive renovation and will probably be closed. Nearby, on the Louisville campus, is one of the castings of the famous sculpture, The Thinker, by August Rodin. According to Wikipedia, there are 28 cast sculptures throughout the world. The first cast sculpture can be found in front of Grawemeyer Hall on the
University of Louisville Belknap Campus in
Louisville, Kentucky. Made in
Paris, it was first displayed at the
St. Louis World's Fair in 1904 and was then given to the city. This sculpture was the only cast created by the
lost-wax casting method. If you stay near the stadium, the statue is within a couple of miles and makes a great photo op.
Many of the other suggestions made by other posters are good choices and you should be able to find plenty of things to fill your day-and-a half of free time before the game.
Enjoy your visit and we hope you come back.