And don't stop there. If you're gonna visit the Alamo, you may as well see the missions along SA's Mission Trail. All the info you need can be found on the San Antonio Missions National Park website Don't miss the acequia at Mission Espada.
It will not take a full day, but I recommend the Witte Museum. It has a great hands-on exhibit of DaVinci inventions. I went last weekend with my kids when we visited San Antonio. It is close to the Zoo, which is good.
I recall a place right next to the Alamo that had a very cool rendition of the battle there, complete with movie snippets and special effects. (laser, smoke, etc.) A really cool way to catch up on a little history and waste an hour. I'd see it again.
While I agree that most state histories can be a bit dull, Texas' history is anything but. Just the fact that we've had six different flags flying over our land makes for some interesting stories. Add the Alamo, the Battle of San Jacinto, tales of the old west, the Civil War, etc. and I think you'll find that we have a rather colorful (and quite bloody) history. I remember taking Texas History in 7th grade, and it's still one of the most interesting classes I've ever had. Sound like you need to visit the Bob Bullock Texas State History Museum in Austin.
When I went to Trinity, we used to always say that the best thing to do in San Antonio was going to Austin.
I'll second this. we ate there a couple of weeks ago on the way to port aransas and it was pretty good. not as good as tookies but in the ballpark
I agree with the Alamo, as well as the Ripley's Believe it or Not museum and Wax Museum, located in the same building a walking distance from the Alamo. I'd definitely take in some Tex-Mex food, as well. There should be plenty to do to take up your time.