We generally do all breakfasts in. Mostly for convenience and because we like to eat a substantial breakfast and head out to the beach as early as possible. Lilly's Market in Coral Bay sells REAL live honest to goodness NYC bagels in their frozen section and they are DAMN good.
English muffins, eggs, bacon, cheese usually round out the breakfast menu.
Genrally villa food consists of breakfast items, snack items, drinks, lunch meat and bread, chicken breasts, romaine lettuce and caesar dressing, as well as a package of hot dogs and buns in case villa gravity or some serious rain precludes us from exiting the villa. Those items generally provide us with some flexibility on meals in if we are too lazy to go out. Otherwise we generally like to eat out (it is vacay after all!)
Keep in mind that grocery pricesa re much higher than you are used to and you should keep your villa meals simple. Otherwise by the time you add in the costs of a lot of extras you might as well have goneout to dinner IMHO.
We bring a few snacks with us to the beach and always a bottle of frozen water (thrown in the freezer the night before)which is usually nice and cold by the time we're ready to drink it.
We also prefer to stay in Coral Bay these days (Cruz Bay just seem s too busy

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Anyway, we stay at the beach until we just get too hot (usually around 2pm) and then head someplace like Tourist Trap, Skinny Legs, or Vies (all in or near the Coral Bay side of the island). IMHO these are MUST visits for lunch.
After a liesurely lunch we head back to the villa for a shower, cocktails and a nap (not necessarily in that order).
After we get hungry again, usually around 7 or so we head out to one of the following (in no particular order):
Island Blues, Miss Lucy's, Shipwreck Landing, Sweet Plaintains, Aqua Bistro or Skinny Legs (if we're feeling like a burger and hadn't already been there that day for lunch).
Cruz Bay has some really great restaurants as well: Some of my traditional faves are Morgans Mango, Fish Trap, or Lime Inn. Of those Lime Inn is more at the top of the list.
For fancier options and a bigger bill at the end of the night you can go to ZoZo's or Asolare.
Casual fare in Cruz bay include:
Uncle Joes or Candi's BBQ (Carry out is best but be patient).
Deli Grotto (for breakfast or lunch -- cash only) They make great sandwiches tp take to the beach. PLus really good desserty type stuff.
And of course the ubiquitous Beach Bar where you will probably run into more forumites than you can shake a fish at.
After so many visits, I really don't mess with the fancier places too much these days and opt for a more casual menu that doesn't include anything with foam (unless it's in my drink!)
There are tons more options but that's just what I could come up with off the top of my head....