For ‘unique to the area’, I’d go with the Maid Rite in Greenville. It looks like a chunk of the ’50’s that fell out of the sky… and that’s because it really hasn’t changed any since then. Loads of character… even charmed my sneering British ‘food snob’ GF. It features their own spin on loose meat (ground beef, supposedly cooked with beer & mustard, topped with onions & pickles) sandwiches.
Plus it has a gum wall: (I can’t post links here yet, but google maid rite greenville, and there’s a youtube video).