Don't bother with Hilton Head. I was over there years ago and aside from a small public beach, the rest of the island was controlled by private, restricted developments. I was over there last year for an afternoon to pick up a Leer topper that a guy was selling and its worse now that it was. Its not the kind of place I would want to vacation or live.
Much of the Florida Panhandle is still in good shape, Hurricane Michael got everything from Tyndall AFB at Panama City, over to Port St Joe, but the rest of it was either not affected or has already recovered.
Oddly everything is the same distance, Dauphin Island, Ft Pickens, and Hilton Head (via I-40 over the Smokies) is 765 miles from the point on the south side of Indy I picked. Hilton Head is 810 miles if you go thru Atlanta to avoid the smokies.
I was at Dauphin Island Alabama, at the mouth of Mobile Bay, last fall, and was quite happy with the visit. (765 mi from the south side of Indy) Depends on what you like to do, but the city owned campground is nice (but could stand some minor things like getting rid of a couple of derelict city trucks that hadn't moved in years, and fixing a couple of issues with their very nice brand new restrooms and showers (water runs out of the shower into the dressing area of the stall). Across the street is the ferry terminal. For $5 you can (on foot or bicycle) ride across Mobile bay and back, and while on the other side, visit Ft Morgan. Just past the campground is Ft Gaines, which is also a nice visit, and also across from the campground is the Estuarium, a very nice aquarium focused on the bay and marine estuary environment of the bay. Adjacent to the campground is a 100 acre Audubon Wildlife and Bird Sanctuary with lots of walking trails and signage. Plus there is a nice beach and pier for fishing.
There is also some good seafood eating on the island.
You also have the Battleship Alabama and associated aircraft and ship displays you can visit on the way down, plus other historical venues such as Bellingrath Gardens.
https://bellingrath.org/https://www.ussalabama.com/http://www.gulfquest.org/http://colonialmobile.com/https://dauphinisland.org/http://estuarium.disl.org/http://mobilebayferry.com/schedule/http://fort-morgan.org/Charles