Here area few other choices:
A couple of things to add for the Houston area are the San Jacinto Monument and the nearby Battleship Texas, both in Pasadena. Kemah Boardwalk-fine restaurants and other attractions-Kemah is in the same general area as Pasadena-south east area.
The Houston Zoo, Houston Museum of Fine Arts, Houston Downtown Aquarium, Houston Museum of Natural Science, Space Center Houston, Minute Maid Park-home of the WORLD CHAMPION Houston Astros
Galveston-Moody Gardens, Galveston Island Historic Pleasure Pier, Bishop Palace, Historic Strand, assorted tree sculptures throughout Galveston (leftovers from hurricanes), Galveston-Port Bolivar ferry ride (free).
If you have interest in industrial areas, Texas City has a large selection of large chemical plants and huge refineries. Very impressive to see at night.
Have fun!