Buxton is a city in Traill County, North Dakota, United States. The population was 348 at the 2020 census. Buxton was founded in 1880…Buxton is a city in Traill County, North Dakota, United States. The population was 348 at the 2020 census. Buxton was founded in 1880. Buxton was founded in 1880 in Buxton Township as a townsite along the Great Northern Railroad in 1880. The post office began operating in November of that year. It was incorporated as a village in 1922. It became a city in 1967, after the North Dakota Legislature enacted legislation that eliminated all existing incorporation titles for towns and villages in the state.