Entering city of Fall River. Fall River lies in an area where the Taunton River flows into the Mount Hope Bay. The Quequechan River flows through the city. The city's name comes from Falling Water. Places to Visit - USS Massachusetts Memorial, Marine Museum, Old Colony and Fall River Railroad Museum, Lizzie Borden Museum, Fall River Heritage State Park, The Carousel at Battleship Cove. City of Fall River to Rhode Island/Massachusetts State Line