Overall groceries are more expensive than the mainland. Since everything is shipped in perishables like milk, bread, cheese, etc. are even higher. Here's a quick run down having recently lived there. Other posters such as Seuss and WJBrandt live there so can chime in if I'm missing anything
CostULess - Big (for the islands) warehouse style. If you want to get a case of pop/soda, chips, giant box of cereal any alchohol (beer, wine liquor) this is the place to go. This is the cheapest place for alcohol. There's another warehouse called Pricemart but you have to pay to have a membership. CostULess is next to the movie theater and home depot.
Plaza Extra- In Tutu Plaza (Center of Island), down from the Big K-mart. This is more of an island version of a large grocery store (Jewel, Alberts, Publix, etc.) Good prices, also have produce.
Marina Market - On the East End in Red Hook. Kind of a combination gourmet grocery and upscale local grocery store. Best place to buy meat (Steak, burgers) on the island. Buy your liquore at CostUless though as it's a couple dollars more here. However if you are on the East End the location can't be beat. Also very good fresh veggie, cheese and fresh seafood selection. Most East Enders just shop here since it's so convenient.
Others:
Pueblo, kind of a smaller version of Plaza Extra
Gourmet Gallery - Just like the name, In Crown Bay Marina and Havensight. Expensive and upscale.
Try the roadside stands for veggies and fruit. Depending on when you are there you can get some great avacado's, bannana's, etc. If Monkey bannana's are in, try them small and very sweet.
Can't help on the BVI but get a Paté or Johnny Cake at Zelma's. It's right next to Customs at the West End. Boy are they good!!
Enjoy your trip!