Was it Woody's? I grew up in Jacksonville and that was the first place I ever had South Carolina style mustard based sauce. I remember it because it was such a sharp departure from the Eastern Carolina style I grew up with.
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If it's the same "Woody's" that's near here, (chain?), it's OK. Really, probably excellent for a chain. They do have the mustard sauce, but since I don't like mustard, I've never tried it. Woody's BBQ`is pretty good without any sauce.
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Checkers is that kind of take-out joint with thin, mustard-vinegar sauce. It's great on the pulled pork sandwiches and ribs. It is a very small hole-in-the-wall joint thst you can also sit down and eat- in. The Friday and Saturday night BBQ and seafood buffet requires reservations!