Depends on what you're into. 1. I like to just hit the road west from S.A., across the limestone plateaus all the way to the Big Bend country, but it's a long drive, and bleak for those who aren't into rock. Keep going west to the Grand Canyon. Long hot drives in summer2. Staying in Texas, make a side trip to Austin for the music scene, then head southeast to Corpus Christi and spend a few days on the beach at Padre Island (there's also a cool research lab and wildlife refuge there) would be a more relaxing way to go.
3. You are not far from the Ozarks/Ouachitas of Arkansas. Lots of green mountains and mountain culture.
4. Head east, catch the Deep South circuit of New Orleans, Natchez, and Vicksburg on the Mississippi.
5. Go for cool high mountains in the Rockies. Head for Durango, Silverton, Leadville, Ouray in Colorado. If I had to pick one of these circuits, that would be my first choice. If you have time, you might be able to combine that with the Grand Canyon target, or make a loop over to our canyon National Parks in Utah--Arches/Zion/Bryce.
Texas has a huge illustrated guide they give away, I would get my hands on that if you want to explore Texas its ownself.