Arapahoe is a census-designated place in Cheyenne County, Colorado, United States. The population was 102 at the 2020 census. Arapahoe was established in 1870. The Arapahoe, Colorado, post office opened on May 5, 1906. The Arapahoe post office has the ZIP code 80802. The town name honors the Arapaho Native American people who lived in the a…Arapahoe is a census-designated place in Cheyenne County, Colorado, United States. The population was 102 at the 2020 census. Arapahoe was established in 1870. The Arapahoe, Colorado, post office opened on May 5, 1906. The Arapahoe post office has the ZIP code 80802. The town name honors the Arapaho Native American people who lived in the area.