Our last couple of times there, we stayed at Braunig Lake RV Resort. Very nice place, very clean and well kept, great people there, and the price is right. They also take Passport America with no restrictions. It's just outside of 410 on I-37. Just north of Braunig Lake. Easy to get to downtown.
We stayed a Blazing Star RV Resort located at 1120 W SL- 1604 N San Antonio Tx. Which is right by Sea World and about 20 min from downtown. Very nice park clean level cement pads, workout room and very nice pool.