Mountains to Sound Greenway National Heritage Area Act This bill establishes the Mountains to Sound Greenway National Heritage Area in the state of Washington. The Department of the Interior shall designate a willing local unit of government, Indian tribe, or nonprofit organization to serve as the local coordinating entity for the heritage area. Such entity shall prepare and submit a management plan for the area and assist federal, state, and local governments, tribes, regional planning organizations, nonprofit organizations, and other interested parties in carrying out such plan.