The closest table I've found to San Antonio is a Verhoeven an hour away at G Cue Billiards near Austin:
G Cue Billiards
300 Hester's Crossing RD
Round Rock TX, 78681
(512) 310-8925
It can get busy at night since there are several players and only one table, but they are a friendly crowd and always welcoming to new players. PM me if you'd like the email of the owner to arrange a game.
Good luck, and let me know if you find one closer since it's quite a drive!
Robert