Moon Island is an island in Quincy Bay, in the middle of Boston Harbor, Massachusetts. It is the location of the Boston Fire Department Training Academy, and Boston Police Department shooting range. All of the land on the island is owned by the City of Boston but the island is under the jurisdiction of Quincy, Massachusetts. It is also part of the Boston Ha…Moon Island is an island in Quincy Bay, in the middle of Boston Harbor, Massachusetts. It is the location of the Boston Fire Department Training Academy, and Boston Police Department shooting range. All of the land on the island is owned by the City of Boston but the island is under the jurisdiction of Quincy, Massachusetts. It is also part of the Boston Harbor Islands National Recreation Area.