I am of course partial to the
Frio Area and plenty of great places to camp, however not sure about the level of primitive you are looking for. I could be wrong but the really primitive places are probably people's land (private). I remember Boy Scout Camps fitting your criteria but probably only for them. You may or may know the Frio Area bc of Garner State Park. It's about an hour and half from S.A. and definitely worth checking out regardless.
However, you will have to check out the Burn Ban.. it's off and on here lately.
Good Luck