In southern Texas the hill country around Fredericksburg, Kerrville, Bandera (cowboy capital of the world) area is interesting. In Fredericksburg, a neat old German town, there is the National Museum of the Pacific War, a very well done museum. And if you like wine there is the wine country trail with a very large number of wineries.
Then over to San Antonio, and the Riverwalk, Alamo, Spanish mission trail, mercado, Buckhorn Saloon/Texas Ranger museum are worth a visit.
The Sonora Caverns in Sonora, TX are a National Natural Landmark are reputed to be very beautiful but I have not been there, yet.
I live in north Texas so I am sure there are those who live in southern TX that can give you more ideas.