I don't know about the grocery store but there is a Hess minimart at the entrance of Boardwalk. It has great prices for milk, water and beer. DH would walk there to replenish his supply.
Well, I *think* that Gooding's is closest, but it's kind of pricey. So I go a mile farther and shop at a very nice Winn Dixie (only a couple of years old).
I agree that Goodings is probably the closest, but I'm a big fan of Publix, so I go to the one just past the Mary Queen of Universe shrine and the outlets. Well worth it to me! Better prices than Goodings and better quality (IMHO) than most others.