Five museums under one roof: the Buffalo Bill Museum covers the life and legend of William Cody with enough critical distance to be interesting; the Whitney Western Art Museum holds serious paintings and sculpture by Frederic Remington, Charles Russell, and their contemporaries; the Plains Indian Museum is one of the better Native American collections in the Mountain West; the Cody Firearms Museum is vast and deeply documented; and the Draper Natural History Museum covers the Greater Yellowstone ecosystem with good diorama work and live programming.
Budget a full day for the complex and you will still be moving quickly. The Whitney collection alone warrants two hours. The combined admission is around $25 for adults and is good for two consecutive days, which is a reasonable deal given the scale. The centre is located a short walk west of downtown on Sheridan Avenue. It is the main reason many visitors stop in Cody rather than passing straight through to Yellowstone, and it justifies the detour.