Mmm...San Antonio is not really that well known for BBQ. When we head down there, we normally just eat Tex-Mex. Dyal_SC made some posts awhile back about his trip down there under Best BBQ Joint. I think he went to Casa Rio on the Riverwalk as well as The County Line. I think he liked the bbq at the county line, but I don't remember being impressed with it. More of a touristy kinda place. If you have time, you could drive up to New Braunfels and try Cooper's. Not sure how good it is. The original out in Llano is/was pretty good, but haven't been in years.
I've heard/read good things about a place called Smoke Shack. It's a food truck and usually located at 2347 Nacogdoches Road. Whatever you do, stay far far away from Bill Miller Bar-B-Que. Nasty stuff. The fast food of bbq. Good luck.
More good Tex-Mex or Mexican in San Antonio. Get to the Hill Country - Kerrville, Fredericksburg ... Out toward Seguin, Gonzales, Luling , Lockhart ... Up around Austin, Taylor, Eglin ... My "bucket list" place is the Taylor Café just for the opportunity to meet Vencil Mares and shake his hand. I use his technique to make my pinto beans.