Of those three, I would also say Somerville. There are both state parks and US Army Corps of Engineers parks to choose from. Both have websites where you can reserve campsites. This time of year, it's a good idea to reserve ahead of time.
If you are willing to drive a bit, then look at Fairfield Lake and Hunstville State Parks, along with the US Army CoE parks at Granger Lake (east of Georgetown, near Taylor). Brazos Bend S.P. isn't too far either, and Stephen Austin S.P. even closer. There is also a state park near Mexia that is pretty good, but I cannot remember the name.
If you haven't been there, you also need to do Enchanted Rock State Natural Area north of Fredericksburg. One of the better tent camping places in central TX, but unfortunately a few hours away from B/CS. Well worth the trip though.