Sunfan, it would be best to rent a car to tour the area. Due to the traffic alone (be prepared) maneuvering a large vehicle would be challenging. There are places you can rent a Jeep and other cars so think about doing that.
Have you found a park to stay at? Make a reservation soon if you haven't. Lots of very nice parks in the area. Check out Pine Mountain. Duvall in the Smokies also. There are many others so you should be able to find something.
The obvious place to go is Dollywood. Nice park and family oriented and some great coasters for the kids. It's not like Disney at all. Dolly's Stampede is probably the best dinner show. Hatfield and McCoys is good too. Lumber jack show is cool. . There's the Aquarium of the Smokies in G'burg. Anakeesta attraction there too. The park itself offers hiking mostly with lots of water falls to see. Climgmans Dome is the 2nd highest point in east. Lots to do and see.