The Alamo is okay, but it's the other missions that make up
San Antonio Missions National Historical Park that are the must-see IMO.
Brackenridge Park, El Mercado, & the Riverwalk.
Head to Austin to tour the Capitol and Harry Ransom Center.
Like Darcy said, the caverns! Loved visiting them...Natural Bridge was my favorite.
Go to Fredericksburg, visit the Nimitz Museum of the Pacific War, hike at Enchanted Rock State Park.
Visit San Marcos & New Braunfels...hit Landa Park, go tubing. And there is always the ginormous outlet mall.
In the winter, eagle watching on the cruise at Canyon of the Eagles (amazing place to stay). And in the spring, you will have to do the bluebonnet tour & photo ops. And you'll need to buy Meg's bluebonnet kit
And if you are wanting a bit of a longer road trip, you could head to Brenham and get some Blue Bell at the Creamery