You'll be able to find plenty to do in the Houston area for a long weekend. As PP said, the Schlitterbahn in Galveston is not the "original" Schlitterbahn that is on all the TV shows. It is a fun waterpark, but not nearly as large as the original Schlitterbahn in New Braunfels.
Moody Gardens is right next door to Schlitterbahn and is a fun place to visit. They have a rainforest pyramid, an aquarium pyramid, an IMAX theather, a 4-d Theater, and Palm Beach (which is a water play area-- great for younger kids).
http://www.moodygardens.org/ We are members at Moody Gardens, so we go a lot

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Space Center Houston is a fun day, as well. Make sure to go on at least one of the tram tours that take you around the actual Johnson Space Center. We like the tour that stops at the super-huge swimming pool where they train the astronauts under water to help simulate weightlessness.
The Kemah Boardwalk has a lot of restaurants to choose from, as well as some carnival-style rides.
http://www.kemahboardwalk.com/
The beach is a tricky subject. The problem with Galveston beaches is that the silt from the Mississippi washes down the Texas shore line, making the water appear "muddy" and not clear. If you grow up here, you're used to swimming in it, but I wouldn't come here and think of the beach as an ultimate vacation destination. When we go to the beach at Galveston, we like Galveston Island State Park
http://www.galveston.com/galvestonislandstatepark/ You can bring in your own canopy, etc. Of course if you're flying down, and will need to rent chairs and umbrellas, I would suggest Stewart Beach
http://www.galveston.com/stewartbeach/
The Houston Galleria is always a fun shopping experience-- lots of high-end stores and an ice skating rink in the mall.
Houston also has a great Zoo (the new Africa part reminds me a lot of AK), and great museums.
Honestly, if it's not that much more $$, I would try to fly in to San Antonio instead. There are a lot more "touristy" options in the San Antonio area-- you could go to the "real" Schlitterbahn, spend an afternoon walking down the River Walk, go to the Alamo, head to Sea World San Antonio, go tubing down the Comal river in New Braunfels, go to Six Flags Fiesta Texas, etc. You can have a couple days of fun in Houston, but San Antonio lends itself to a "family vacation" much better. Just my 2 cents. Have fun whatever you decide. --Katie