Sponsored Topics. Sugar Mountain is a village in Avery County, North Carolina, United States. The village is located on Sugar Mountain's north slope. The population was 226 at the 2000 census. Sugar Mountain is located at 36°7′28″N 81°52′32″W / 36.12444°N 81.87556°W / 36.12444; -81.87556 (36.124444, -81.875555).