I'll mention all that I know of being open.
BZH
Oasis
Big Fish
Infinity @ Oyster Bay Beach Resort
Quai Ouest
This is a pretty complete list at moment other than adding a small little place called Le Pause that serves breakfast and lunch. It's located across from the entrance to the wrecked Captain Olivers. Also add Bread n Butter which sells wonderful croissants in the morning and has rotisserie chicken in afternoon. Located next to Oasis. Owned by the same people.