Rather than loading up the boat with tons of food for the week, is it naive to think that I can get away with buying some essentials to get us going (and for emergencies when we can't get to shore) and then buying food where the locals buy food on the various islands that we visit? They have to buy food somewhere, correct?
Our preferred way to travel is to wander around neighborhoods, eat where the locals rather than tourists eat (OK, we will be going to Foxy's) and see how people in other countries live. Isn't there street food available?
I've been sailing the BVI since 1982, first on charters and since on deliveries and my own boat.
The biggest issue you will have with your concept is that there are few places within reasonable walking distance of most anchorages to do much fill-in purchasing except for canned goods and some odd frozen bits. On the smaller islands many people plan their shopping around monthly trips to Tortola and use the same delivery services charterers do to have food put on the inter-island ferries to pick up at the dock.
For a big basic shop at the beginning of your trip I strongly recommend ordering ahead from one of the big three provisioning companies for delivery to your boat. You won't regret it, especially for heavy stuff like water, drinks, and alcohol.
Ample Hamper was the first of the yacht provisioning company. After many years as the only game in town--and good reviews--they have faded a bit. Their on-line ordering system was still pretty good the last time I looked.
Bobby's Marketplace is a major player in grocery in BVI. The provisioning department is in the main facility in Roadtown and fills orders as food comes across the loading dock so you will get the best they have to offer.
Riteway / RTW is the other major player in grocery. Some things are better at Bobby's and others at RTW. The biggest difference is that the Bobby's online presence is easier to navigate.
What you buy depends in great part on your itinerary. You can do a bit of fill in shopping in Spanish Town, North Sound, East End (Trellis / Marina Cay), Great Harbour JVD, and West End (Soper's Hole). The only good place is in Soper's. I have phoned in an order to Bobby's to pick up in Trellis Bay or Cane Garden Bay.
As I said on the chat I do suggest carrying your own spices from your own kitchen to avoid the expense of buying whole jars of spice. The exception is for curries and peppers -- Sunny Caribbee has some great choices and I bring curry powders back every trip. Bring tea bags if you have a favorite. Personally I avoid traveling with coffee because of the association with drug trafficking; call me paranoid if you will but I do try to avoid fitting into profiles.
A lot depends on food preferences of your group. Big breakfast/light lunch crowd or opposite? Recognize there are some realities of the subtropics, such as the rapid deterioration of bread.
You've said you're going for seven days.
Let's walk through a trip and consider the implications. You have lots of time to think about this -- if you get a food order in a couple of weeks ahead you'll be fine.
First day out of Roadtown I like to go to Cooper Island. My thinking is that it is a pleasant close reach for a couple of hours, gets you a bit upwind in Sir Frances Drake Channel, and avoids the crowd starting the same day as you who flock to Norman Island. It is also the best sunset in the BVI. Grab a mooring and head into the Beach Club. We usually have a couple of drinks and an appetizer and head back to the boat for dinner, but your group might stay for dinner ashore. You know your folks better than we can; talk it over.
Day 2 - breakfast then leave for the Baths. Earlier is better to avoid other charterers and the cruise ship crowds if a ship is in port. Check the schedule - let me know if you can't find it. I take an NPT ball at the far South end and land my crew on the beach at Devils Bay before tying the dinghy to the dinghy line and swimming in. You'll go through the Baths in the reverse direction of most people but it just doesn't make any difference. Walk up the hill afterwards for lunch at the Top of the Baths and then walk down the hill on the other side to Devil's Bay. Sail to Marina Cay or Trellis Bay for the night. There is a Pusser's Restaurant on Marina Cay that is decent with a great view. The Last Resort Restaurant on Bellamy Cay in Trellis is fun if a bit loud for my taste.
Day 3 - breakfast then leave for snorkeling at the dogs. Something for lunch on the boat afterward that is easy to eat in hand during your afternoon sail to North Sound. Anchor off Mosquito Island or Prickley Pear, take a mooring at Leverick Bay or Saba Rock, and settle in. My choice is usually to anchor and eat aboard. If you want to eat ashore my choice would be Leverick Bay but Saba Rock is nice also. BEYC is expensive and over-rated.
Day 4 - breakfast aboard and start for Anegada between 8.30 and 9. You'll want high sun your first time into the anchorage there. Make dinner reservations for lobster (not my favorite but something everyone should do once - they are more like giant crawfish than Maine lobster). Some people like Anegada Reef Hotel or even Potters better. Pick one. Grab a cab to Cow Wreck Beach and have lunch there. Ask for Walker Magnum and tell him Dave on Auspicious says hi if he is on island. Cab back to the harbor.
Day 5 - breakfast aboard and head Southwest toward JVD. This is your big sailing day. Lunch underway. On the 32 you have reserved I'd squeeze in some time on Day 4 to bang together some tuna salad or something. If you have eaten dinner aboard and chose to make chicken you could have made extra and make chicken salad. Mid-afternoon or earlier you should make Sandy Spit which is worth a visit for a romp on the beach. Head into Little Harbour and grab a ball. Dinner aboard or at Sydneys or Harris. Alternatively head into Great Harbour for Foxy's or Corsairs.
Day 6 - breakfast aboard and hop around the corner to White Bay and lunch at Soggy Dollar Bar. Sail to Norman Island and have dinner and drinks on the Willy T or Pirates or both.
Day 7 - breakfast aboard, get lunch ready and sail back to Roadtown. There's no magic bullet here, but it should be clear that food and itinerary are linked. It should also be clear that the provisioning packages from the charter companies are too big for just about everyone, and don't recognize people's individual tastes.
There are as many answers as there are people.
My suggestion is to get your crew together a few times as your plans progress and keep them involved. That's part of the fun and anticipation.
You'll have a tough time making bad decisions.