I used to live there. My favorite outdoor range was Bracken. It's on the northeast side of 1604, just exit Rolling Oaks and make a right on Nacogdoches. It's just past bracken drive on the North side.
As for gun shops, grew up in Converse (just outside of Randolph AFB) and frequented O'Reily's off of Pat Booker and McKee's gunshop/gunsmithing on I believe windsor road. He's an excellent gunsmith and a Vietnam vet (USA Ranger).