If you're staying in town to do this, I'd say to try to get a hotel room at a nice place downtown. Then go to the Eiteljorg museum, actually go to the monument on monument circle, take a carriage ride, eat dinner at St. Elmo's or something.
If you can swing it - maybe go to someplace a couple hours away like Louisville. Then stay at The Seelbach or The Brown - go to Hillrich and Bradsby (the people who make the bat's), go on a dinner cruise on The Star of Louisville (www.staroflouisville.com), maybe even go to Huber's Winery and Orchard in Starlight Indiana (www.huberwinery.com) and while you're on the north side of the river, go to Schimpff's Confectionary in Jeffersonville (www.schimpffs.com)...the confectionary is pretty well known for their cinnamon red-hots, and modjeska's, but they have a lot of different chocolates to choose from and turtles and a candy-museum where you can watch them make things; They also serve lunch and ice-cream. Also - you can visit Locust Grove (www.locustgrove.org) George Rogers Clark lived there with his sister for a while. You could also go on a cruise on the Belle of Louisville (it's a steamboat) (www.belleoflouisville.org).
For what it's worth - and good luck!!