Hot Springs is a city in and county seat of Fall River County, South Dakota, United States. As of the 2020 census, the city population wa…Hot Springs is a city in and county seat of Fall River County, South Dakota, United States. As of the 2020 census, the city population was 3,395. In addition, neighboring Oglala Lakota County contracts the duties of Auditor, Treasurer and Register of Deeds to the Fall River County authority in Hot Springs.