Guadalupe State Park is pretty good. It's close enough to both Austin and San Antonio that you can have a night out. It's also on the banks of the river so that you can go tubing. (Or a short drive to Canyon Lake for the commercial tubes)
Possum Kingdom is kind of cool if for no other reason than the adrenaline rush provided to us by the Toadies. Good fishing there.
Texoma is decent...but too close to Oklahoma for my tastes.
Close to Dallas area is Dinosaur Valley State Park (Glen Rose) good campsites, nice hiking and dinosaur tracks are kind of neat. Near Austin, a favorite is Pedernales Falls State Park. Can go into Fredricksburg if you want for a bit of shopping/eating/beer drinking or wine tasting.
When it gets cooler, Tyler State Park just outside Tyler is great. Beautiful pine trees and a nice lake to camp near. Love that area.
If you want to check out the only natural lake in Texas, check out Caddo Lake near Jefferson.
I'm going to be putting up feeders, a deer stand, and cutting a road through mesquite in 98 degree weather this weekend in Mills County if you are interested. I'll bring the beer, the chiggers, sunburn, and blisters are also free.