As has been mentioned there are a few places to shot in Tennessee. I would add to that Oak Ridge and Tullahoma (AEDC) are two of the best shooting facility's anyone could hope for. The folks in Oak Ridge go out of there way to make a new guy feel welcome and they are glad to see you there. Jim Sokolowski in Tullahoma also puts on a "Very" good shoot both are to be commended for the way they run there shoots.
There are also are a couple more shoots in Tennessee, Memphis has a Mid Range (600 yds) F-Class match every month during shooting season, they also have two regional match's a year, this is another place were they are glad to see and help out new shooters. I do realize that Memphis is not middle Tennessee, but what the heck it's a nice drive. If you are interested in shooting from the bench from time to time ( great trigger time) there is a VFS match every month in Gallatin, Tn as well, these are shot from 100 to 300 yds.
As to Blakeley, Ga they have a great range, I personally however wouldn't recommend this place to my worst enemy. It is the complete opposite of the other places mentioned. There are some other F-Class type match's around Atlanta but I have no information for them.
Roland