If you don't want to go to Nashville, Bowling Green is an hour and a half away. The Corvette Museum and factory tour were fun.
http://www.corvettemuseum.org/plant_tours/index.shtml
There was also the Lost Cave. Kind of interesting but overpriced.
http://www.lostrivercave.com/cavetours.html
A little further is Mammoth Caves Nat'l Park, which is fascinating. Nearby Land Between the Lakes is nice but not the time of year for outdoors.