Last year I stayed in San Antonio. Transport (by rented car on the new toll road) was pretty painless (never encountered any substantial traffic), but it’s a pretty long drive. This year I am going to try to get a bit closer. Lockhart was mentioned earlier — I’d stay there just to be closer to some good barbecue ;)
Also, if you’re driving, the prepaid parking with shuttle at the airport worked VERY well; the lines for those buses were far shorter than the other shuttles.