Welcome to San Antonio, I was born and raised here. Like Texason and Skibane wrote, there are no free ranges here. If you do happen to find one please let me know.
There are two more places. One is called A Place to shoot, which is on the south side off loop 410 and Moursund and the other is called Black Hawk Range which is off Jarrett road. Unfortunately both I believe charge by gun.
Hey Skibane, I stopped going to bullet hole because it seemed they were always changing their policy on the type of bullets one was shooting. One week it was ok to shoot full metal jacket, but the next week they wouldn't let me shoot. There was another incident that made up my mind that I would not be going back there.
RNYC goes to a place outside of Bandera TX, that is very friendly.