Fall Creek Falls and LBL. I will have to add Indian Boundary to my list of places to visit. With a family, state parks are typically always a good bet.
Fall Creek Falls. Savage Gulf State Park. Your car may not be next to your tent, maybe 50-100 yards away. Beautiful rim hikes and you have Stone Door as well.
My favorite new place to go is Gee Creek along the Hiwassee River.
Rock Island State Park, Tim's Ford SP, Barton Springs campground in Normandy, Long Branch campground on Center Hill Lake, Happy Camper in McMinnville and Horseshoe Bend in Rock Island are all great.