Robinson's wharf is a restaurant and seafood dealer that is right down the road, Southport general store has a deli, and Newagon Inn has a restaurant, which are all on the island. Also, the taxi cabs in the area will deliver your food!
Yes, there are a handful on the island, mostly seafood based (but they have other stuff on the menu as well). If you are looking for delivery though, you will be out of luck, as nobody delivers here.
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