The Jekyll Island Club was called "the richest, most inaccessible club in the world" by Munsey's Magazine. The Club House is now the Jekyll Island Club Hotel and the hotel and 33 other historic structures on 240 acres have been designated by the National Park Service as a Historic Landmark District. Even if you don't stay at the hotel, you can visit the museum and take a historic tour, plus visit the Georgia Sea Turtle Center.
If you go:
Located near Brunswick, Jekyll Island is one of the barrier islands designated as part of the Golden Isles. In addition to the historic district, recreation opportunities abound: golf, biking, birding, fishing, swimming and more. Other hotels as well as a campground with primitive and RV sites provide accommodations.
Links:

Riverview Drive
Jekyll Island, Georgia 31527 USA
Mailing address:
Jekyll Island Museum
100 Stable Road
Jekyll Island, GA 31527 USA
Phone Numbers:
Jekyll Island Museum
+1 (912) 635-4036
+1 (912) 635-4036
Georgia Sea Turtle Center
+1 (912) 635-4444
+1 (912) 635-4444