Sheepdogs,
I highly recommend Jekyll Island Campground, Jekylll, Island, GA. We spent nearly a week there last February.
It's just South of Brunswick, GA, off I-95, exit 29. A few miles on Hwy 17 gets you to the Jekyll Island Causeway. The Campground is large, and the sites are VERY large. Live Oak trees tower above, providing a filtered shade just about everywhere. The island has miles and miles of beaches, and due to a day use fee to use the causeway, it's not bogged down with traffic during th off-season.
Here's the URL for the Campground, which also leads to maps and the whole Jekyll Island vacation planning schtick.
http://www.jekyllisland.com/camping.phtml
We were in the "E" area, but "G", "B" and "F" are equally nice. The CATV was a nice bonus.
Hope your trip is a good one!
Denny_A