There are several venues for matches in San Antonio, these are the ones that come to mind (and the names are linked to the web sites)...
River City Shooters - Blackhawk Range on the SW side of town. I've shot IDPA with them and loved it. Great group of guys, very friendly and very safe. Highly recommended.
Texas Tactical - Run by "Iron Mike" Webb up at Cedar Creek range just NW of SA. Mike runs IDPA, Carbine, Night/Lowlight, Shotgun and Three Gun. Very popular and well run from what I have heard.
Bullethole - On the westside of town, probably the closest to SA. I haven't shot a match there but I have shot at their ranges, and all I have to say is I hope they run their matches better than they run their ranges! No safety officers or supervision, and I have personally witnessed numerous violations that should have resulted in people being removed (such as handling weapons while the ranges is cold and people are checking their targets). I will only shoot there on weekdays when there is less of a crowd, but I still try to avoid the place. But I do know people who shoot there, and even someone who works there, that like the place so "your mileage may vary."
Your best bet would be with the Texas Tactical group. I have shot with Mike's group for over a year and would highly recommend it to everyone.
There will be a carbine shoot this Saturday at the Cedar Ridge range, if it doesn't rain heavily again, gate opens at 0745 to let Mike in the range and all those who want to help set up the different stages. Parking can get tight so it's best to help set-up. Range opens at 0900 and we start shooting between 0945 and 1000. I won't be there this Sat. due to work but I will be up in Austin for the shoot at ARC this Sunday.