I'm from Texas, and have been to Galveston plenty of times, and I dont think its a beach worth visiting at ALL. We go to Florida if we want a nice beach =)
If you want to see Texas, I would suggest San Antonio, Houston, Dallas, or Austin instead. Or Ft Worth. San Antonio seems the most touristy =) One of hte best waterparks in the US is in New Braunfels, which isnt too bad of a drive from San Antonio. You could always visit Houston and drive to Galveston if you wanted... its on 45 min south to hit it.
Just don't expect too much =)