Webster is a city in and the county seat of Day County, South Dakota, United States. The population was 1,728 at the 2020 census. The to…Webster is a city in and the county seat of Day County, South Dakota, United States. The population was 1,728 at the 2020 census. The town was platted in 1880, and was named in honor of J. B. Webster, a pioneer settler.