Fairfax is a town in Osage County, Oklahoma, United States. The population was 1,555 at the 2000 census. Site of the infamous Osage Indian murders. Fairfax is located at 36°34′17″N 96°42′23″W / 36.57139°N 96.70639°W / 36.57139; -96.70639 (36.571386, -96.706259).