The Wyoming State Capitol is located in the city of Cheyenne. Cheyenne is the seat of government for the U.S. state of Wyoming, also hosting the workspace for the governor, and his staff; Mark Gordon. Built between 1886 and 1890, the capitol is located in Cheyenne and contains the chambers of the Wyoming State Legislature as well as the office of th…The Wyoming State Capitol is located in the city of Cheyenne. Cheyenne is the seat of government for the U.S. state of Wyoming, also hosting the workspace for the governor, and his staff; Mark Gordon. Built between 1886 and 1890, the capitol is located in Cheyenne and contains the chambers of the Wyoming State Legislature as well as the office of the Governor of Wyoming. It was designated a U.S. National Historic Landmark in 1987. The Capitol underwent an extensive three-year renovation and reopened to the public on July 10, 2019.