I highly recommend you make the 30 minute drive Northeast of SA to Lockhart, TX. Texas BBQ is considered by most to be the best BBQ in the US and Lockhart has the 2 best BBQ places in the state...hence, they are the best two BBQ places IN THE WORLD.
The Greatest Barbecue Restaurant in the World - Slate Magazine Just keep in mind that they close early (6pm) and aren't open on Sunday.
And since you are half way there, you might as well continue on your journey to Austin which has the state capital, the University of Texas, and a great downtown bar scene. A great side trip would be lunch in Lockhart, see stuff in Austin that afternoon, party on 6th street that evening, then drive back to SA the next morning (stopping back by Lockhart of course (remember it is the two best BBQ places in the world).
While in SA, in addition to the Alamo, there are 4 other historic Spanish missions. Mission San Jose is probably the best. Make sure you check it out if you haven't already. Back during the Great Depression, the US government fully restored the mission as a jobs program. Make sure you take the free guided tour, they have 3 or 4 a day and you can see the schedule on the Mission San Jose website.