There is a 20-30 acre open, sandy field near Blythewood (35 miles south of the Chester exit) that people ride often. It is one of those "implied permission" areas...you know, they hain't runned me off yet, so I muss have permission!
There is also Manchester SF near Sumter that has 18 or 19 miles of trails and a sandy MX track.
If you don't mind the drive, Hell Hole (sandy and not maintained well) might still be open near Batesburg/Leesvile.
Turkey Creek near Edgefield is similar to the track at TNT, but faster, with easier jumps.
One of the bike shops near Charlotte is supposed to have a track and I think one of the local pro riders also built a track between Chester and Charlotte, but I haven't been to either of those.