Angoon is a city on Admiralty Island, Alaska, United States. At the 2000 census the population was 572; by the 2010 census the population h…Angoon is a city on Admiralty Island, Alaska, United States. At the 2000 census the population was 572; by the 2010 census the population had declined to 459. For statistical purposes, it is in the Hoonah-Angoon Census Area. The name in Tlingit, Aangóon, means roughly "isthmus town."