La Salle's La Belle ship excavated from Matagorda bay and in a museum in Austin-
https://www.thestoryoftexas.com/la-belle/the-exhibit
Washington on the Brazos historic site-
http://wheretexasbecametexas.org/ Not a lot to it but interesting if you're in the area.
Nasa space center in Houston and the Houston museum of natural science are pretty good.
San Antonio is obviously the Alamo and Mission San Jose.
Make use of tripadvisor.com to find places to eat, lodging, etc. Make sure to get some good BBQ while here.
atlasobscura.com can be a good site to find small, interesting places in your travels.
https://www.atlasobscura.com/things-to-do/texas#browse
When will you be here? There are some seasonal things that might be of interest. I'm about 1.5 hours away from you, in College Station if you get in a bind and need someone to bail you out of jail.
That's just next door in Texas distance.