I can vouch for the Knoxville area. If it isn't the shooting capitol of the south, its darn close. We have the world-class Oak Ridge Sportsmen Association which has a multitude of ranges including 1000 yd. high power rifle, indoor pistol, 200 yd rifle, plinking, archery and trap and skeet. You join as a member by the year for $100.
Next is the John Sevier range in the city of Knoxville on Rifle Range Road. It has a 100 yd rifle range with NRA rangemaster in charge, a pistol range, and a shotgun range. Highly recommended for the $5 per day. Only open certain days of the week.
If you don't mind the general public, there is a 200 yd. rifle range in Norris, TN about 20 miles north of Knoxville. $5 per day. No range master.
Then, there is Guncraft in Knoxville, right on interstate 40. A great gun store with indoor pistol range. You can join or pay by the session. You can even rent and fire a submachine gun!