Between Savannah and St. Augustine is Jekyll Island, GA. There's not a ton of food options on Jekyll Island, but there are a few decent restaurants, The Wharf being one of our favorites. A short drive to St. Simons Island yields a lot more food options.
Jekyll Island was called the Millionaire's Playground back in the early 1900s. The country's wealthiest spent their winters on Jekyll Island. The Jekyll Island Club Hotel was their home, except for those that built their own "cottages" on the grounds. Those buildings are still used today. You can visit the museum and get a guided tour of the historic district. There is the Sea Turtle Center and there are miles of hiking trails and biking trails.
About 1 hour west of Jekyll Island is the Okefenokee Swamp. There are multiple entrances. We like to go to the National Wildlife Refuge entrance outside Folkston, GA. It is more self guided, but they do offer boat tours and you can rent Kayaks (or bring your own) for the best way to see the swamp. There are lots of hiking trails. There is also the Chesser Homestead, that offers a glimpse into the life of how folks lived in the swamp. There is a $5 entrance fee here.
The Okefenokee Swamp Park entrance in Waycross does offer boat tours, a train tour, an education center, alligator viewing areas and a short boardwalk to a viewing tower. There isn't much that you can do for free here.
If you can get a campsite reservation, Hannah Park in Jacksonville is a great County Park. The beach is a short walk or bike/car ride away. It won't be as warm as further south in FL, but definitely better than Virginia.
Between Jekyll Island and Jacksonville is Amelia Island/Fernandina Beach. There are a lot of restaurants here on the beach as well as in the "downtown" area.
-Michael