depending on location of you home base in Texas........most state parks are great places to camp. You posted a picture on the beach in Galveston. If you like the beach areas, one we enjoy is the Lower Colorado River Authorities Camp Ground at Matagorda Nature Park.
It sits right on the Colorado River as it dumps into the bay. There are Kayak trails in the park and they do rent equipment if you don't have your own. The nature center has programs they put on and you can tour the center. Off of 2031 the road leading to the park there is access to the beach via Beach Rd to Dunes Rd. People camp out on that beach. You have to purchase and annual pass as I recall it was somewhere around $10.
Consider picking up the Texas Public Campgrounds Directory. I've found them at the Texas State Welcome Centers or at some local Convention & Visitors Bureaus in tourist towns. It will list all of the state, federal and local gov't facilities. COE campgrounds are great as well as some "jewels" that are city run parks.
pass along your travel experiences, were are always looking for new places to explore