Can't think of many with authentic Caribbean vibe in Maho or Simpson Bay. Simpson has some great places but not the "vibe". Most of those places would require a drive. But as, you probably know, you will find that in Grand Case. Add Ti Coin Creole to your list in Grand Case. Restaurant family owned and recently reopened after storm damage serves authentic food.
The restaurant at Belair hotel Little Bay would require a drive but good food, feet in the sand.
I think you'd do better to just eat at Mary's Boone that first night. My opinion.
.
