Planning A Trip

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.

There are various Florida state parks along Interstate 10 in the panhandle. Florida state parks are generally well kept and a good place to stay. You see the signs for the exits to take to them routinely as you drive east across the state. I can only relate personal experience with one: Falling Waters near Chipley, FL. It was nice, but the sites were challenging for our fifth wheel. As I read your signature information, you may have an easier time. It was not a big park, but contained scenery you would not generally picture for Florida.
Be sure to reserve any Florida state parks well ahead of time. You can do it on line.

The FL state park we camped in was Blackwater River SP, in the panhandle. Beautiful park, inland so less popular than the beachfront ones. Our site was HUGE - we had a 34' TT at the time and there was way more than enough room for it and our truck, and not hard to back into. FHU site. I'd recommend it.

On the panhandle in Florida we stayed at Big Lagoon further east we were late making a reservation and were not able to get into Ft Clinch so we stayed at Stephen Foster Memorial right on the river. Nice park, large lots although not full service.

In SC there are four ocean front state parks. Hunting Island, Edisto, Huntington Beach, and Myrtle Beach. Now is the time to make reservations because the full service sections of Myrtle Beach and Huntington Beach all fill up quickly.

If you want to stay close to I-95 Santee and Givhans Ferry are good options. Here is a link to SC state parks: https://southcarolinaparks.com/

I would assume when you head north from FL you will be taking I95. If so, Jekyll Island in GA is a really good park, plus they have FHU which is nice. The campground there is beautiful with the spanish moss. As mentioned earlier in an above post, James Island in Charleston, SC. James Island is ran by the county and is a really neat park. FHU as well. Minutes from downtown Charleston but a very secluded campground. Both Jekyll and James Island have tremendous paved bicycle trails that run the entire perimeter of the island.

I think you might find the Ultimate Public Campgrounds very useful. it provides info on over 41,000 public camping spots. No commercial/private campgrounds are included. Apps are available for iOS, Android and Mac devices.

If you should be in the area of St Augustine, I can recommend North Beach Campground...the beach is right across the highway...we stayed there a few years ago and really liked it. Most all the sites have privacy. And if you've never been to St Augustine, you can get tickets for a trolley that takes you all over town...it's a hop off and hop on with lots of stops.

Your trip sounds wonderful!