Stanley is a city in Buchanan and Fayette counties in the U.S. state of Iowa. The population was 81 at the time of the 2020 census. Stanley …Stanley is a city in Buchanan and Fayette counties in the U.S. state of Iowa. The population was 81 at the time of the 2020 census. Stanley is located at 42°38′31″N 91°48′43″W / 42.64194°N 91.81194°W.