South Padre Island
Travel time: ~6-hour drive, 55-minute flight from Houston
At Texas' southern tip is South Padre Island, and when it isn't acting as the state's spring break capital, it's a beautiful beach haven for families. The beaches here are clearer with whiter sands and less seaweed, so the sights are much different than what you find in Galveston. It's home to its own Schlitterbahn with resort lodging and indoor and outdoor attractions, the South Padre Island Birding and Nature Center for your wildlife buffs, and the world's largest sandcastle.

Corpus Christi
Travel time: 3-1/2-hour drive, 1-hour flight from Houston
This beach town isn't as far south as Padre, but the beaches are similarly nice because the seaweed (and crowds) are sparse. The area is not very touristy but is home to some truly unique spots, like the USS Lexington - a WWII aircraft carrier and naval museum - the Texas State Aquarium, and the South Texas Botanical Gardens and Nature Center. Oh, and like all of Texas' big beach towns, there is a Schlitterbahn water park (as well as Hurricane Alley Waterpark). There are also plenty of museums and parks to visit if you're just over the whole waterpark shebang. 

Burnet
Travel time: 3-1/2-hour drive from Houston
Drive about 30 minutes northwest of Austin and you'll find the quaint town of Burnet. Two of my favorite Texas state parks are in this small city - Longhorn Cavern State Park, which is a gateway to beautiful underground caverns that make you feel like you've stepped off the planet (or at least outside of Texas), and Inks Lake State Park, which has some of the best swimming spots the state can offer. Lake Buchanan is also nearby as well as the Eagle Eye Observatory, which houses two telescopes and is inside Canyon of the Eagles resort.

New Braunfels
Travel time: 3-hour drive from Houston
New Braunfels makes for an amazing vacation spot for many reasons: its natural surroundings feel completely foreign from Houston's muggy flatness, and there is no shortage of things to do. You can't go wrong with the original Schlitterbahn Waterpark, which has rides and attractions for kids of all ages; or Natural Bridge Caverns, where you can tour Texas' beautiful underground; or find a spot to enjoy the stunning and refreshing Comal River. Even though it is a small town, there is even a children's museum nearby as well as unique shopping and eating opportunities downtown.

Port Aransas
Travel time: 3 hours and 45 minutes drive, 1-hour flight from Houston
For families who enjoy fishing, Port Aransas is your spot. The beaches are hardly ever crowded, and the local seafood restaurants are delicious. There's Mustang Island State Park where you can spend the day or spend the weekend camping, the Port Aransas Nature Preserve at Charlie's Pasture and Leonabelle Turnbull Birding Center for nature enthusiasts, and the massive pier at Roberts Point Park for fishing and just...relaxing.

Waller and Brenham
Travel time: 30 minutes to an hour from Houston
I lump these together because there may not be enough at each town to warrant a full weekend getaway, and because they are so close together and in the same direction out of Houston they make for a good pairing. Waller is home to the Lonestar Jellystone campground, which is a stellar stop even if you're not staying the night. The campground has a ton of amenities from a huge playground to the miniature waterpark. In Brenham, cool off at the Blue Bell Creameries factory and enjoy the historical city's parks or Washington on the Brazos, which is a living history museum.

Top photo: Splashing around at North Bayfront Park in Corpus Christi/Photo courtesy Corpus Christi CVB