Maynard is a city in Fayette County, Iowa, United States. The population was 476 at the time of the 2020 census. Maynard is located at 42°46′…Maynard is a city in Fayette County, Iowa, United States. The population was 476 at the time of the 2020 census. Maynard is located at 42°46′28″N 91°52′42″W / 42.77444°N 91.87833°W on the Little Volga River.