Obviously you have the choice of one route on the way down and another route back. I go online to the various states travel and tourism web sites and research what there is along the way. I can also recommend the Biltmore estate in Asheville. Plan on a full day there and downtown Asheville is interesting too so a couple days there is not too much. If you have never been to Gatlinburg, Pigeon Forge, Sevierville then I say its worth a stop for 3 to 4 days. Dollywood is a great park to visit too. Many dinner shows to take in along with entertainment venues like the Smoky Mountain Opry. Chattanooga (and Gatlinburg) has a great aquarium and Lookout Mountain and the incline railway.
You may find that there is more to do than time permits. Happy and safe travels.
