We have traveled to Pigeon Forge (Gatlinburg/Sevierville area) TN. I love TN. My kids really enjoyed themselves - as we are not big beach people either (except for the gulf beaches and islands). There was a lot to do - but it was in fact about a 10 hour drive. I wish we had started going earlier and made a tradition of it, I think the whole area offers much to do:
Hiking, shows, rafting (as they get older), pools, shopping, historic areas, great scenery, gatlinburg aquarium and ripleys.
We rented a chalet in the mountains and that alone was great. Hottub on the deck and game room. http://www.sugarmaplecabins.com/ was who we rented from - but you can see from their site some of the views.
I admit it was a long trip down, but worth it. We left on a friday after work and spent the first night in Virgina to break up the drive.