Buckley is a city in Pierce County, Washington, United States, founded in 1882. The population was 5,114 at the 2020 census. Buckley sits bel…Buckley is a city in Pierce County, Washington, United States, founded in 1882. The population was 5,114 at the 2020 census. Buckley sits below Mount Rainier and is well known for hosting the annual Log Show.