Greetings! One town that has a very "old Fl" feel to it still is Grayton Beach. It's a very southern town that you can walk around and go to the beach. They have several restaurants there and access to the bike path on 30A. I recommend the Bed and Breakfast place for breakfast. You don't have to stay there to eat there. And look for souvenirs at The Zoo gallery.
Thanks! Tricia