Quick Advice on Short Trips from your town:
Start close to home. Do the really close stuff first. Look for festivals, state parks and sporting events. And obviously the beaches. Not entirely a bad idea to just roll down the coast hitting beach towns along the way and stopping when you get to Padre. Skip the refineries obviously..
My Must Sees:
1) San Antonio – Tex-Mex is unreal, History of Texas begins in the Alamo. Your son will like SeaWorld. Riverwalk is touristy but worth a first visit, skip the Menger Hotel and Stay at the Emily Morgan. With a young son, this should be your first bigger trip.
2) Big Bend- This is a major trip. Need 4 days at least. 7 hour drive from your place. You’ll have to pace yourself to do this, and I realize it might be on the backburner, but it’s the most unique thing everyone misses.
3) Galveston-Kemah-Johnson Space Center. Pretty Self Explanatory. Beaches in Galveston are decent, Kemah has some nightlife. And the Johnson Space Center is a must.
4) Drive North on Highway 281 From San Antonio. See Fredericksburg, Circle Back to Austin, Come Back Through New Braunfels. Stay nights in the small towns. It’s quiet. Roads are scenic. Towns are unique.
Just a few. Extremely biased picks, I tried to be conservative. The truth is there is a lot to be said for exploring your interests and curiousity and just going from there.