There are a number of relatively large facilities in the state. The few that come to my mind are:
Middle Tennessee Sporting Association -- Dixon Springs, TN
Montgomery County Shooting Complex -- Clarksville, TN (see note below)
Dead Zero Shooting Park -- Spencer, TN (see note below)
Oak Ridge Sportsman's Association -- Oak Ridge, TN (see note below)
Unknown #1 -- Seems like there is a good-sized facility around Jackson, TN but I can't remember what it is.
Unknown #2 -- Same as above for Memphis. I even shot there once but can't remember the name of it.
Montgomery County Shooting Complex note: MCSC is a large facility and has individual ranges for a lot of venues. Several of their ranges are closed right now (and have been for a good while). My understanding is that they are doing lead abatement on some of their facilities but I could be wrong.
Dead Zero Note -- Dead Zero is probably one of the largest facilities in the state, and also one of the most expensive for some venues. They have a huge site and could easily work in some bullseye pistol if you could convince them of it.
Oak Ridge Note -- ORSA is an old, established site and is members-only except for match days. I've shot USPSA there several times without being a member. It's a large facility, 1,000 yard rifle as I recall, but I don't know how much of the site is actually in use.