I will start with museums.
There are museums in nearly every city and small town.
Fort Worth has several museums on a variety of subjects from science to cowboys, all within walking distance of each other.
Houston, Dallas, San Antonio, Corpus Christi and Austin also have many museums.
Odessa has the presidential museum, the Meteor Crater, and an art museum. The presidential museum is for all the presidents. The small town of Wink has the Roy Orbison museum. Midland has the petroleum museum which is all about the oilfield.
Several cities also have zoos.
The best in my opinion are Fort Worth, Lufkin, (my great uncle's train engine is there too), Tyler, San Antonio, Abilene and finally Victoria. Those are from best to worst in my opinion. Dallas also has a zoo but I have never visited it.
Amusement parks.
Six Flags over Texas. It is in Arlington. That is between Dallas and Fort Worth. Many other things to do there including the Ripley's Believe it or not museum.
Astroworld in Houston.
Fiesta Texas and SeaWorld in San Antonio.
Schlitterbahn in New Braunfels, Galveston and Padre Island.
There are several aquariums in Texas. I didn't like the one in Dallas but Corpus Christi has a nice one and Rockport has a small free one with all native to the area species. They also have the Texas Maritime museum.