Jekyll Island

Jekyll Island, which is a state park in its entirety, is a nice place to explore. It has a slight feel of a tourist trap but not completely. Its historic area is the best place to start. Have lunch or dinner at The Wharf with its breezy outdoor seating and indoor seating by huge windows looking out on the salt marshes and handsome Sidney Lanier Bridge. Then walk on the lovely paved walkways past the various late 19th century mansions called "cottages" and impressive Jekyll Island Club Resort with its fairytale three-story turret. It was built in 1888, and its members included such notables as Rockefeller, Pulitzer, Morgan, and Vanderbilt. The first transcontinental telephone call was made here, to Alexander Graham Bell. Also, the secret weeklong discussion that resulted in the creation of the US Federal Reserve happened here in 1910. The Great Depression and then World War II took a toll on the Club and its last season was 1942 when it was closed early because of the difficult labor situation during the war. The state of Georgia purchased the entire island in 1947, including the Club.

Meandering around the paths, you will come across Faith Chapel, a little church you can enter, Island Sweets Shoppe, an ice cream shop with a plain interior, and Georgia Sea Turtle Center, which has tanks for rescued sea turtles but is quite crowded and all indoors and costs $10 each to enter. 
The loveliest part about walking around are the huge oak trees strung with Spanish moss, the flowers, and the architecture of the Club and cottages.
Bike riding is the main activity on the island. You can rent bikes in this area at Jekyll Wheels, and then bike anywhere you choose, along the wonderful paved trails shaded by moss-strung oak trees and other tropical plants. There are very few road crossings along the paths. You can bike to Horton House, the ruins of a house, on boardwalks over swamps, and to the various beaches.
One beach is Great Dunes Beach, with nice sand dunes that you can view from the boardwalk (these are a little oil-streaked), and dark, hard-packed oil-streaked sand at the shore, and murky water. Driftwood Beach has huge driftwood trees strewn across the beach.

Directions

The Wharf Restaurant, 370 Riverview Dr, Jekyll Island, GA. There is plenty of free parking here. 

Georgia Sea Turtle Center, 214 Stable Rd, Jekyll Island, GA 31527.
Open daily 9-5. Closed Jan 1, second week of Jan, Thanksgiving (fourth Thurs in Nov), Dec 24, and Dec 25. 
Cost to enter is $9 for adults, $8 for seniors aged 62+, and $7 for children aged 4-12.

Click on map for interactive view