Well I can tell you about Alabama. There is no law prohibiting open carry in the state of Alabama while on foot. You must have a permit to carry a loaded firearm in a vehicle concealed or not. For reference see Attorney general opinion 1984-205.Great link.
I was planning a trip to Florida and I can carry everywhere. What is a little frustrating and will take more research on my part, is the issue of open v concealed carry in Mississippi and Alabama. I'm thinking that I'll probably just carry concealed there anyway being that I don't have a holster for open carry anyway.