[link|http://www.galveston.com/visitorcenter/|Galveston Visitors Guide]
[link|http://www.moodygardens.com|Moody Gardens] - very neat place. Has a tropical rainforest in a glass pyramid, complete with birds, fishand butterflies. 3D-Imax, Imax ride(fun). And an interactive science museum. I like to bring people here.
Depending on when you're here, [link|http://www.dickensonthestrand.org/|Dickens on The Strand] could be fun. [link|http://galveston-online.com/strand/|The Strand] is the historical downtown Galveston. It's been made touristy with lots of interesting shops. One of my faves is the candy store(don't recall the name) that has a soda fountain in it. I normally get a cherry phosphate then watch them make candy using early 1900's machines.
[link|http://www.lsfm.org/|Lone Star Flight Museum] is next door to Moody Gardens.
I broke the suggestions into seperate posts so others could add more suggestions for each city and they'd be grouped when you check them out.