Kemah Boardwalk, Galveston
Sadly, much of Kemah was destroyed by Hurricane Ike. The pictures are amazing. You can find them online. I'm not sure when Kemah will be back to normal. Please check the website for updates.
Kemah Boardwalk is about an hour from Houston (including traffic). It is a miniature version, however, so if you are expecting the works don't get that excited. However, for a day/night away from the city it's a great solution. There are rides for children (even a new roller coaster), fun restaurants, shopping, and all while listening to (and smelling) the gulf. Most of the restaurants have live music, too, on the weekends. Kemah also have a few hotels available if you want to make a weekend trip out of it!
I would definitely recommend it for a family trip!
I would also recommend looking at their calendar of events on the website while planning your trip to Houston because they often have celebrations (usually towards each holiday), concerts, and special occassions which you can have fun with. Most are centered towards kids but others focus on guys (Houston Texans, race car days, etc).
*When you first find your way there you will see some cheap parking prices. My advice would be to go directly to Kemah's parking. It is free and we have always been able to park there. Some people assume there aren't any paces and then end up paying $5-$10USD when they could have parked a whole lot closer and cheaper. Save that money for a pina colada! :)