The Danish Mill is rather new on the island and it didn't take long to get us hooked.
It's family owned and operated.  They make almost everything from scratch.  The baked goods are fabulous.  We LOVE the cream puffs, napoleans, and almond tart.  Oh, but there's even more...pies, doughnuts, breads, and cakes.  You must stop in every day to see what they've baked for the day.  They also make delicious sandwiches.  I personally love the reuben.  Their soups are wonderful too.  The kids had the swedish meatball and dumpling soup once and it was superb!  They offer free Wi-Fi and have a covered deck in back.  Or, you can sit in the grass under an umbrella.  It's filled with locals and tourists alike.  It's a great stop to pick up picnic food.  And there are so many places to picnic on the island.  You know how small the island is when locals have noticed how many times you've been frequenting it lately....umm, that's embarrassing.