Below are some of the best beaches for dogs to visit in Georgia: 1  Jekyll Island, off the southern coast of Georgia near St. Simons Island, welcomes dogs on the beach as long as they’re on a leash. St. Simons Island allows dogs on leashes (or off a leash if they’re under the immediate control of their handler) during the summer between Beach Access Points 1-6. After Labor Day, dogs are allowed at all the other Access Points as well.