We like Myrtle Beach State Park better than most of the commercial parks in the MB area, as long as you get a decent site (stay away from site 66!). Of the commercial parks, Ocean Lakes is nice.
If you have time, check out Hunting Island State Park on your way from MB to Savannah. Some sites are tight but the Appalachian and Florida campers had a rally there a few years ago and had a great time.
Try River's End Campground in Tybee Island. Close to Savannah and the beach. It was private when we were there, now it's city owned:
City of Tybee Island - Campground.
Near Destin, try Topsail State Preserve. It used to be a private park but is now state owned. We have never been able to get reservations there due to its popularity, but others say it's exceptional.
Have fun!