Florida has a number of history oriented State Parks along the east coast in between Jacksonville and running south of St Augustine. Includes an old sugar mill and an old fort
Map fo Florida State parksBulow Plantation is the mill, and I guess the fort is a federal park, there are four in the Jacksonville/Augustion area. The big one is Castle San Marcos in Augustine. That map is a lotless useful than it used to be before they 'improved it'.
The walking tour of St Augustine itself is full of history in a highly commercialized fashion tho.
But FL is littered with historical sites. I'm less familiar with the Pensacola area but there is that Naval Air Museum there.
Going east down I-10 you'll pass Florida Caverns (worth a stop but pathetic compared to the Federal caves) and a number of other state parks with a history theme.
Coming down I-75 Georgia has a lot of historical sites, Andersonville for one around the interstate.