San Antonio is known for it's great Tex-Mex food, not really a BBQ paradise. There are also many great steak houses as you are in the middle of beef country.
If you are going to the Air Force Base avoid the bbq place there. I went there once and we left without even eating half of our food, it's really bad.... I've been by there a few times just to see if anything has changed, sadly it hasn't. I guess they do well because they have a captive audience of trainees who cannot leave the base.
For Lunch I would Suggest
Congers Smoke Shack
347 Nacogdoches Road
They are only open from 11:00 AM to 3:00 PM or until they are sold out.
it's just off the south inner-loop under the highway. It's a trailer with a couple picnic tables with great food. I have eaten at this location several times, but have never tried the second location. NOTE: If you want your brisket without sauce, you have to order it that way. They also add feta cheese to the coleslaw.
Another good place is
Rudy's
15560 Interstate 35 Frontage Rd
Near Live Oak, TX but still part of San Antonio. The food here is good, not outstanding, but good. I have eaten at both locations and there is an obvious difference between them, this is the better one.
If you have an extra day and want to visit the greats, I would suggest renting a car and traveling to Lockhart, TX and visiting Kreuz Market, Smitty's Market, and Blacks. Or you could also travel to Austin and hope you get in early enough for Franklin Barbecue, or John Mueller.
But my all time favorite was Salt Lick BBQ in Driftwood (slightly closer than Lockhart).
Hope this is some help to you....
Added: There is also a few good places in New Braunfels, Cooper comes to mind, but it was many years ago since i have been to New Braunfels.