DNR has ranges open to the public throughout the state. I think all have pistol and 100 yard rifle ranges. They are kind of Fuddy, though. The one in Spartanburg has a 200 yard rifle range but you shoot through a concrete tunnel (to cut down on crossfire?). Wear earplugs and ear muffs!
I belong to a range just over the GA line with a 400 yard rifle range but the waiting list for membership is over 300.
Clinton House Plantation has a 1,000 yard range and shoots to a mile but the mile isn't open full time. I think it's once a month.
There is also a club in Belton but I don't know much about it.
Welcome to the upstate!