A landmark piece of America's history I don't know if it needs much explanation. It is just a short walk away from the riverwalk, and even if you don't go in you can take pictures of the exterior and some statues they have built in front.
If you love roller coaster this is a good spot to check out last year it opened the steepest dive coaster in the year. It's about a 25 min drive from the downtown area.
Seaworld is a fun mix of rides and aquarium. I haven't been to this one, but the ones in San Diego and Orlando were good. There is enough there to fill your day but not rush. It's about a 30 minute drive from the downtown area.
One of the oldest saloons in Texas this place is just fun to take a peak into. They also have some fun souvenirs to buy, and a museum about the Texas rangers and cowboys. We haven't had the food there though so can't vouch for that part!