Welcome estone. Perhaps Huntsville State Park would be good for you. Large wooded sites and loads of them. Should be able to find privacy? Also Brazos Bend State Park.
www.tpwd.com is the adress I believe?
National Forest wood be great as they allow camping most anywhere and fires ar o.k. The problem is hunting season!!!
Fairfield has a primitive site 3 miles in but the sound of the power plant sucks?
State parks will probably fit the bill the best.
Lots of great camping close to Houston. When I lived there that was all that kept me going!