I'm starting with the essentials...food.  Bring it with, no really, the amount of money you'll save is amazing. But, if you just must shop like a local, whenever possible we use The Market Place, not King's Market.  Same owner, cheaper, just going outside of town, but well worth the extra effort.  Employees at either place are great.  Their cheerful and friendly, they'll talk to you.  To get to this store, here are the confusing local directions.  Head down Spring Street, that's the main street...when you get off the ferry it's that first left, you'll go by that cool bar (we'll talk about that later, it's the Front Street Ale House...a must stop.) and up the hill, continue on past the grocery store on the right, through the three-way stop and past the gas station.  Continue on up the hill and past the four-way stop.  When you see the Best Western, across the street will be a street and a coffee shop, take a left and start watching on your left.   Big Parking lot in front.    This is the store.  Best prices, in the dairy section there are usually two shopping carts with markdown products.  Random things, food, cleaning supplies, baskets.......While there look for Abe and Lumpy in the produce section.  You'll enjoy their company, stop say hi...you sort of have to, it's just not grocery shopping without doing it.  Bathrooms are at the front of the store.  Nice cut flowers, (but the best cut flowers are Rolf's he pushes the little cart around town on Fridays selling his own.  Their beautiful), lots of choices, but reg and organic, largest meat department (King's market in town is the place to go for all your seafood needs, unless you go down to the market/shop with the live tank on the docks..way cool.), bulk...and the best prices compared to anywhere else on the island.

A little tip grocery shopping on the islands is the same as shopping in the real world, the dog stays outside, you have to wear shoes and yes there are credit card machines...you may charge to your hearts content.

If it makes a difference Kings has baggers when you checkout, at The Market Place you selfbag, oooh.