There are five dive shops in San Antonio, the one that I recommend is Duggan Diving,
http://www.duggandiving.com/.
Well, if you want to go to Corpus Christi (3 hours, each way) there's one dive that you'll want to make, an oil rig dive. Even though the tour/dive boats shut down around mid-October, you can find any number of captains looking for charters. You can contract through the two major Corpus dive shops, Copeland's
http://www.copelandsinc.com/, or Ascuba Venture Inc.
http://www.ascubaventure.com/. All depends on the weather and seas. Don't pay anyone in advance, just call the day before your scheduled trip and find out if the captain is going out - if not, you don't lose anything, and you don't have to make the drive.
Texas has great rivers. In Central Texas two of them are especially dive-friendly, the San Marcos, in San Marcos (45 minute drive), and the Comal in New Braunfels (25 minute drive). Each town has a good dive shop: The Dive Shop
http://www.divesanmarcos.com/, and Makai Divers
http://www.makaidivers.com/index.html. The water conditions remain the same throught the year, including flow rates, as both rivers are fed by springs and are not heavily influenced by a lack of rain. The trick is to enter the river and swim upstream, use half of your air, and float back down.
At the San Marcos there is a dive program offered, many serious local divers take it, info here:
http://www.diveaquarenasprings.com/scientific.html.
The above dives are done by most all local divers sooner or later. If you want to dive Lakes Canyon or Travis, just contact a dive shop, they're diving both every weekend.
Save room for BBQ...