A few years ago I visited a friend in Lousiville, Kentucky. This is where the Kentucky Derby is held, so you can visit the racecourse. There is a paddle steamer on the Ohio river and on the Indiana side of the river there is a park with exposed fossil beds. There is also a baseball bat museum which has the worlds largest baseball bat outside it, a huge cavern, a zoo, the most amazing cemetery and this fantastic cafe
http://www.lynnsparadisecafe.com/. And it is Mohammed Alis birthplace. I went in January and I think I was the only Brit there - my accent was certainly commented upon nearly everywhere!
But don't go to Florida without visiting at least one theme park. They are so well done. Believe you me, they are nothing like the British ones. They are so clean and well thought out. At Islands of Adventure as you walk into the Jurassic Park part the theme tune is playing and there are 'fossils' built into the walkway. And the Cat in the Hat bit has to be seen to be believed, you can even get green eggs and ham there!