In Brunswick, GA there are two campgrounds that meet your needs.
Coastal Georgia RV Resort has about 20 back in sites along a small private lake that is well stocked with Bass and Bream. It has a pool, a conference room with kitchenette and it has a really nice outdoor pavilion at the end of the lake side sites. It's about 2 miles off I-95 about 20 minutes to Jekyll Island and 25 minutes St. Simons Island. The resort is fully paved, asphalt roads and concrete pads. There are trees/shrubs between sites. It is a popular park for rallies. The FMCA recently had a rally there.
Blythe Island Regional Park and Campground is at the same exit as Coastal GA RV Resort, but it's about 7 miles or so off I-95 (heading away from Jekyll & St. Simons Islands). This is more of a State Park. Their lake side sites are not directly on the lake like Coastal GA's are, but they are maybe 50-75 feet from the lake. They have about 20 lake side sites. The lake has a swimming area as well as boat and kayak rentals at a reasonable rate. They also have a boat ramp for small boats with electric motors. There is also a boat launch on the Turtle River. There are like 6 pavilions available for rent. The larger ones have grills and sinks.
We go to Blythe Island with our Motorhome for day trips a lot. We live about 10 minutes away. We park the MH in the beach parking lot, open the slides and the awning, hook up the RVQ (only grill they will allow at the beach area), fish and boat in the lake right by the camper. They have walking and biking trails.
Both parks are Full Hook-ups with WiFi and Cable. If Satellite is important then Coastal GA RV Resort would be a better choice. Blythe Island is under a lot of tree cover.
Brunswick is about halfway between Savannah, GA and Jacksonville, FL; about an hour drive to both.
-Michael