The Texas State Aquarium focuses on Gulf of Mexico and Caribbean marine life, with dolphins, sea turtles, shorebirds, reef exhibits, and rescue stories that connect directly to the coast outside. It sits on North Beach, close enough to pair with the USS Lexington if you have the stamina.
Families will get the most out of it, but it is also useful context for anyone heading to Padre Island or Mustang Island. Go early in summer; indoor air-conditioning is part of the appeal by mid-afternoon.