There is so much to do all over the state. I have a special place in my heart for San Antonio because my grandmother lived there, so I got to visit there quite a few times.

Sure there is the Riverwalk and the Alamo, but there are many other Spanish Missions that you can visit in the area. The San Antonio Zoo is really cool, along with the Sunken Gardens (which have been closed for renovation, I don’t know when they open again.)
Mi Tierra is kinda looked down upon because it is touristy, but they have great food, and afterward you can visit their bakery with all kinds of great pastries. It is attached to El Mercado, which has lots of souvenir shops. (As a kid we always went to the Alamo and El Mercado/Mi Tierra if we didn’t go anywhere else. Now when I go to visit, I always try to make it to Mi Tierra.)

If that isn’t enough stuff to do, Austin, the live music capital of the world (and capital of Texas) is about an hour to the northeast, and the Hill Country is up US-281. Fredricksburg is a great little town (I recommend Fredricksburg Brewing Co. to eat and have a local micro-brew).