Some of ones SDaniel listed we've driven past but didn't stay but we have stayed at Bryn Mayr @ St. Augustine Beach. It's on the beach but tight roadways and lots of park models.
On the Gulf side is a park, now "Turtle Beach" @ Fiesta Key, just S. of Sarasota that's nice and on the beach, very tight though and by all means have a reservation.
The panhandle has only Camping on the Gulf @ SanDestin. Fairly nice but tight and the few "beachfront" sites are $$$ w/o fhu. Think Topsail Hill or Henderson Beach (no pool) but have a reservation.
Dave