The Big Duck in Flanders (just outside Riverhead)
Once upon a time Long Island was known for a couple of things and one of them was ducks. This is a locally famous landmark with an interesting tale and makes for a good side-trip.
While you are out there if you're looking for a good place to eat (that is even kid-friendly) try Diggers in downtown Riverhead. It's a pub but the food is amazing. My favorite is the blackened chicken sandwich. So good.