We went for a week last month. First time I'd stayed down there and I had a really good time. We rented one of the cottages kind of up by driftwood beach. The beach at the cottage wasn't anything great, but their pool / clubhouse was nice and it was hard to get my 6 y/o out of there...
For food / drink, I really liked Silver Bluff Brewing in Brunswick, they had a trailer out front selling pizza and it was one of the better things we ate the whole time there. A close second was the Wharf, It's at the Jekyll Island Club / Historical area and was really good. It's right by the Georgia Sea Turtle Center which was really cool, we got to watch them put a GPS tracker in a snake. We parked there and then walked all around that little area and did lunch. We did Tortuga Jacks one night for dinner, the food was ok but I'd go back for the service, our waitress was awesome. We did the Wee Pub, which was really good. That little area has a bunch of shops and stuff as well. It looked like they were putting in a splash pad, so that'll be fun when it's done. We also went to the Beach House Restaurant and Tap Room, which was my worst experience. The food wasn't very good and they did not have any beer. The waitress said that the taps were down and just gave us the bare minimum effort, I got a big vibe that they don't much care for repeat service.
The Jekyll Market was a good store, everyone is friendly and they had anything we needed.
We went to St Simons one day and went to Porch, it continues to be one of my favorite places down there. I really wanted to try Barrier Island Brewing but they weren't open when we went over there.
Make sure you get your parking pass ahead of time. When we got to Jekyll it was insane getting on the island. We sat for about an hour to go three miles to get to the entrance to the island.