Good Morning,
I love to spend time in Tennessee. What time of year are you going? We like to go to Pigeon Forge every year or so. It's about a three quarters of an hour in the opposite direction of your travel from Knoxville. There are four or five outlet malls there, go kart places, Dollywood, shows, shows and more shows, and then there's Gatlinburg, which to me is like Clifton Hill in Niagara Falls. However, this is not really on the way to Florida and you could spend your whole vacation there. Therefore I would recommend the Lost Sea at Exit 60. It's an underground cave. Takes a few hours to go through. It's a nice way to break up the day though.
If you're going in the fall the mountains are absolutely gorgeous when the leaves are changing colours.