Davenport is the county seat of and largest city in Lincoln County, Washington, United States. The population was 1,703 at the 2020 ce…Davenport is the county seat of and largest city in Lincoln County, Washington, United States. The population was 1,703 at the 2020 census. As the seat of government for the county and its largest population center, Davenport serves as an important hub for business, medical and educational services in Lincoln County.