In south Texas Balmorrhea State Park and Palo Duro Canyon state park are nice.
In Denison TX we like Lake Texoma Corps of Engineers park.
If you have plenty of time there are beautiful state parks in Arkansas. We like Lake Catherine State Park in Hot Springs and DeGray Lake state park near there.
Petit Jean Mountain State Park is also nice.
In southeast Missouri Sam A Baker State Park is one of our favorites. No cell service is the only negative. But they do have pay phone and internet access at the office.