Big South Fork is pretty cool, but if you're gonna be in Knoxville and you've never been to the Smokies, then you have to do that. There's plenty of great overnights you could do there. If you want company at night, leave your tent in your car and book a reservation at one of the shelters on the AT (going out of Cades Cove or Newfound Gap is pretty logistically simple). If you want to see less people, do something in the Cataloochee area of the park. There's plenty of trails all over and it's pretty easy to link them together in loops. Near Atlanta, check out Amicalola Falls.
Also, if you've never spent much time in the south and you have time, you should head to Savannah from Macon in Georgia then down to Jacksonville. That's a very very cool area. And you can check out St. Augustine near Jacksonville if you want.