Stonehenge and Sequoyah National are both solid and not too far. Stonehenge is quite tough while Sequoyah has some crazy holes. There are also two public Nicklaus courses that were built in the late 90's that are within a short-ish distance. I preferred Harrison Bay to Cumberland Mountain, the latter being closer to Knoxville.
None of those four courses will blow you away with amenities if you care at all. Unless they remodeled, Stonehenge is straight out of Caddyshack, while Sequoyah is a basic clubhouse and range. The clubhouses at the Bear Trace courses are even more basic buildings just slinging beer and hot dogs.
Sweetens Cove is showing sold out but you could watch as we get closer and maybe people will give up their passes. It's steep now at $125 bucks, but that is to play there all day. It is definitely worth it despite me hearing the experience has changed a bit with it gaining so much notoriety.
Here is the thread I made for a trip across Tennessee that a buddy and I took in 2019.
https://texags.com/forums/60/topics/3028062