You mentioned Central Texas. There is no better time to visit, especially around Fredericksburg than April. We prefer the KOA at Fredericksburg. Inks Lake State Park is ideal but may be difficult to get a reservation even now. I often try for a couple of weekday nights then supplement with something like the KOA. There are also some nice choices around Kerrville.
You might enjoy a visit to our part of the state--Northeast Texas. Springtime is also a beautiful time to visit here. There is Tyler State Park, Daingerfield SP, Bob Sandlin SP, and Atlanta SP. Again, it might be difficult to get into Tyler SP, but my comment above also applies here--try a couple of weekday nights. It would be worth it.
There are two COE lakes which have excellent campgrounds: Lake 'O The Pines with Buckhorn Campground and Brushy Creek Campground. There is also Wright Patman Lake with my favorite, Spring Creek Campground. Atlanta SP, mentioned above, is on Wright Patman.
