Every State Park near the gulf in the panhandle is nice and all have great beaches... but if you think you are going to get a place for more than a night or two or three from Jan to Ap 1 I think you will be mistaken, as most fill up a year in advance. St. George Island, St. Joseph Peninsula, St. Andrews, Grayton and Topsail SParks are all very nice campgrounds with great beaches.
Last year went to Manatee Springs near Cheifland, west of Ocala and it was nice and nearly full in February. Ochlocknee SP, near Sopchoppy was also nice but more primitive and not full in March last year. Usually spots are open at Stephen Foster Cultural Center SP near White Springs. This is a very nice camp ground.
Pressnell's RV and Marina between Port St. Joe and Cape San Blas is small but right on the water, and often has a spot or two open.
I hope some of these work for you.
2014 Shamrock 183
2014 RAM 1500 SLT Crew Cab HEMI 3.21 8 Spd 4X4