NANTUCKET
Nantucket is a special place to me as I worked as a caddie at Sankaty Head golf course when I was 14 and 15. If your boat is docked here you will most likely be at the Nantucket Boat Basin Marina located in downtown Nantucket Proper. Your options for provisioning are a bit limited but you should be able to find everything you need to stock your galley (at a price)
Super stop & Shop
This small grocery will have almost everything you need and is only a block from the marina. This will be your best bet for quick provisioning while on island. Their website offers shopping and delivery by ordering ahead although I have never used that service from them.
Bartlett's Farm
This local farm has been in business since the early 1800's and has over 125 farmed acres on the island. They operate a grocery and deli and their produce is used in almost every restaurant on the island. This is a cool place to get fresh veggies and nice cheese for platters. Check out their website as it has all they carry and the farms entire history.
NANTUCKET BOAT BASIN
167 raw
In business since 1978 167 Raw is your best option for fresh seafood on the island. In season they generally have a great, fresh selection on hand but if you have a special order give them a couple of days to put it together.
Sayle's seafood
Sayle's seafood is a complete retail fish market offering a wide variety of fresh and frozen seafood from around the world. They specialize in Nantucket Bay Scallops, Native Nantucket Lobsters and Atlantic Sea Scallops.
Glidden's Island Seafood
This old school mid Island seafood market promises the finest variety of local and "fancy" seafood available. I did notice on their website that they offer quahogs, that might make it a worthwhile trek to check out while on island.