The obvious place would be the Alamo, which is the most famous Texas icon. Be sure to check out the gift shop in the back. Pee Wee had a really good time there and so will you. You can get the kitsch-iest souvenirs there.
The Alamo comes to mind first,....but Texas is a big state. I live in Dallas so I would say the JFK museum in downtown Dallas (where JFK was shot)
Southfork RanchJohnson Space Center (NASA)
San antonio duh!!!!!!!!!!!!!