Jamestown is a census-designated place in Tuolumne County, California, United States. The population was 3,433 at the 2010 census, up from 3,017 at the 2000 census. Formerly a California Gold Rush town, Jamestown is a California Historical Landmark since March 16, 1949. It is the home of Railtown 1897 State Historic Park and the Sierra Railwa…Jamestown is a census-designated place in Tuolumne County, California, United States. The population was 3,433 at the 2010 census, up from 3,017 at the 2000 census. Formerly a California Gold Rush town, Jamestown is a California Historical Landmark since March 16, 1949. It is the home of Railtown 1897 State Historic Park and the Sierra Railway, which operates steam passenger trains.