Some suggestions, not necessarily in order..

Daytime and any evening other than Sunday--Dreams at Nettle Bay. French, upscale. Generally expensive, but for lunch, you can get more inexpensive things like pizza and sandwiches.

Daytime and evening--Calmos in Grand Case--French but much more casual. Toes in the sand, lovely view of Anguilla and of the sunset. Relatively inexpensive, choices like kabobs, ribs, etc.

Evening only--Ocean 82 in Grand Case--French, very upscale. Relatively expensive. lovely view of Anguilla, faces the sunset, but this time of year, sunset will be over before you dine.

Evening only--Bistrot Cariabes in Grand Case. French, very upscale. Relatively expensive, no view, but a long time favorite of ours, great service.

Daytime and evening--Paradise View-looks out over Orient. French, not as upscale as most of the others, relatively inexpensive, eclectic menu, including crepes.

Enjoy!