My family moved to Texas about 3 years ago. We live between San Antonio and Austin so we do lots of exploring around these parts. We also like to take road trips and explore other parts of Texas. Depending on what you mean by active would help figure out where to go- does that mean out doorsy like hiking, being on the water, or does that mean historical sites, or amusement parks. For outdoor stuff I would definitely recommend the Hill Country area which is basically between San Antonio and Austin. It is an area you will get hiking, beaches, city life all in relative close proximity. There's many state parks, exploring caves, tubing in rivers. My are younger thatln yours, but some of the things we enjoy, in no particular order:
-Johnson Space Center
-Houston Aquarium
-Houston Natural History Museum and Planetarium
-Galveston (add a few days cruise!)
-Port Aransas beaches (or go further south for better beaches in Brownsville)
-Canyon Lake ( popular between March and October for boating and fishing)
-New Braunfels is famous for tubing
-Wimberley- cute town, blue hole swimming areas
-Just about any lake in the area for boating, camping, fishing, tubing
-Austin for Lady Bird Johnson Park, see the bats emerge from the bridge if you come in the summer
-Fredericksburg for shopping and WWII museum
-Johnson City for LBJ birthplace
-Dallas for the Botanica Gardens, JFK Memorial/Sixth Floor Museum
-Grapevine for cute small town and good eats on main street (best time is around Christmas)
-Palo Duro State Park (called the grand canyon of Texas)
-Monahan Sandhill State park to slide the sand dunes
-Amarillo, Midland, Odessa
-Others mentioned San Antonio for the Riverwalk, Alamo, Sea World etc. Personally I stopped taking out of town visitors to those locations as most in my group find them boring. The Riverwalk is pretty at night I suppose, but i find the area dirty. The Alamo has the history but the site is not what most expect I think. Sea world is a nice park- half day unless doing the water park too.
-Catch a rodeo just about anywhere although some area seasonal it seems
-Hit several Buc-ee's just for fun. The ones in New Braunfels, Bastrop (east of Austin), Denton (Dallas) are huge.
-Blue bonnets blooms mid March- April. They're everywhere and so pretty.
I could go on and on with the things to do in Texas. Clearly it's a big place and it takes a while to get from place to place. I'd say define active and that'll help decide where to focus.
Whatever you decide, enjoy your trip!