These are all state (or regional) parks where we have stayed and would stay again:
Fairview/Riverside near Madisonville, LA
or
Fontainebleau State Park just down the road at Mandeville
Buccaneer SP in Waveland, MS
Gulf State Park in Alabama
Fort Pickens in the National Seashore near Pensacola, FL
I would mention St. Andrews SP at Panama City but getting a reservation there is next to impossible
Blythe Island Regional Park near Brunswick, GA
Skidaway Island State Park near Savannah, GA
James Island near Charleston
Newport News Regional Park in Virginia.