I think Cam was suggesting the smaller Peublo near Crown Bay and not the one over by Havensight. From the CYOA dock(in the middle of French Town) to the Crown Bay/Sub-base area is a much quicker trip than the other direction enjoying glacial traffic speeds towards Havensight. Peublo could supply some staples but I would highly reccommend Gourmet Gallery for any fresh foods like meats, fruits, veggies etc. Their prices will be much higher but the quality will be also.
I also second Cam's suggestion to spend the extra couple of hours to get to the BVIs (don't forget clearing through customs) you will not regret it once you are there. Sailing and navigation are easy and in the summer you will have no problem with the crowds that most charters are used to. St John is nice, I frequently sail over there for day trips but whenever I plan to sail for more than a day, the BVIs are more enjoyable.
Lest I forget, Jody's advice may be more important than any other regarding provisioning.
GOT RUM?