There are two main grocery stores within walking distance of 'downtown' Cruz Bay - Dolphin Market and Starfish Market. Personally, I'm a fan of Starfish as the market and adjacent deli/liquor store provide one stop shopping for anything you may need. As for delivery, I'm not sure but it's been my experience that the rental agency you are dealing with MAY facilitate delivery for you. We've stayed in both Grande Bay and at a private residence and each time we were given the option of pre-ordering and having our provisions delivered.