Which of the following institutions is located in Cheyenne?

The Capitol is indeed located in Cheyenne, which serves as the state capital of Wyoming. This building is significant as it houses the Wyoming State Legislature and the offices of the Governor and other state officials. The Capitol is not only a functional hub for government activity but also a symbol of Wyoming's political history and heritage.

The other institutions mentioned serve important roles within the state but are located in different places. The University of Wyoming is in Laramie, the Wyoming State Hospital operates in Evanston, and the penitentiary is situated in Rawlins. Thus, identifying the Capitol in Cheyenne highlights its central role in state governance and administration.