Loads of state parks in central Texas...take your pick!
Have never been to either of your choices, but have 'heard' good things about C.O.T.E.
As noted, Choke Canyon SP - Calliham unit is the one you'd want to camp. The South Shore unit is not nearly as nice...and is currently open for day-use only, so it's academic anyway. I've camped the Calliham unit on 3 occasions in as many years and it is a great park for wildlife viewing.
Further south near Mathis is Lake Corpus Christi SP...another very nice park.
Be aware, Snowbirds will be making their way down around the time you intend to camp, so these parks may be busy until they reach the valley.