Super Food
A great dutch supermarket is Superfood. They are located on the northern side of the island and great fresh breads. great selection of cheeses, meats and fruit. Also has a wine and liquor shop. A fresh fish shop and botch (pharmacy) are located outside the super market.
Another option is Ling and Sons. They are located closer to downtown Oranjestad. They accept American Express and will deliver groceries to your door for a small fee. They stock many American favorites and have an excellent selection of wines.