Believe it or not, this little island has surprisingly complete grocery stores. Notice I did not call them supermarkets, although they call themselves that.
At the outskirts of Cruz Bay, along the road to the South Shore, we have Starfish Supermarket at the Marketplace, which is the largest of our stores. Well-stocked, including a deli section, fresh fruits and vegetables and meats (much more expensive than you are used to), and a good liquor and wine selection. Good parking. You can get sandwiches to go if you want to get to the beach without making lunch yourself.
Dolphin Market is downtown, close to the center, and is a little smaller, but also has good produce and pretty much everything you will need on your vacation. Only a few parking spaces out front.
There is an excellent deli in Mongoose Junction with a great selection of fresh items. Grotto Deli.
Every T'ing at Gallows Point is a large sundry store with a good variety of items.
There are several bakeries, notably Baked In The Sun on the top floor of The Marketplace, and a smaller one at The Lumberyard Complex, C & D Bakery.
You can get pizza all day long at Ronnie's in Boulon Center in Cruz Bay, plus nightly at Cafe Roma. Also, try the pizza on the beach at Senorita Pizza (Wharfside next to the Beach Bar), or two nights a week in Coral Bay next to Donkey Diner.
A few small sundry stores, but don't count on them to have much selection. A couple have recently opened up in Cruz Bay. They seem to be pretty good.
If you are in Coral Bay, you have a few choices, mainly Love City Mini-Mart (favored by locals, a bit crowded, not much fresh produce or meat), or Lily's Gourmet Market at Coccolobo (I like this place). Lily's is about to open another store in Coral Bay.
You can get liquor anywhere. Prices of spirits are much lower than stateside, but wine is much higher. We always say that the mixers cost more than the liquor here, which is why you get such stiff drinks in the local bars. For example, a fifth of Cruzan Dark Rum is usually about $4, and a 12-pack of coke is about $6.
For a discount liquor purchase, try Mixology Warehouse in Cruz Bay on the road going from the Customs Dock and Post Office up the hill towards The Lumberyard. On the left, pretty close to the bottom of the hill. Oops -- Mixology is now closed. Plenty of other places. Remember -- the liquor is very cheap. It's the mixers that cost a lot. That's why the drinks in St. John are so strong.
And expect to buy ice and bottled water at the stores, which most of the locals do, instead of relying on the quality of the tap water.