The Sun Dance is not a tourist event. Neither the Arapaho nor the local people of Wyoming promote it as such. It is done by the Arapaho for the Arapaho themselves. If you would like to visit the Reservation and see dancing, a powwow is probably the best event to attend. Powwows are much less religious, and are attended by many different people from all over. They are promoted by the organizers, and many vendors are present, so attendance is actually desired and encouraged for all people who are interested. There are powwows at least twice a month usually during the summer.
The Sun Dance is not closed to outsiders, however. One may attend and watch, provided one is respectful and obeys all the rules and restrictions in place at the event. A fair number of non-Arapahos do usually attend the event. Many of these are members of other Native American tribes, who enjoy attending other tribes' ceremonies. Some non-Indians do attend as well, mostly as guests of the various Arapaho families. People without connections to the Reservation or without knowledge of such ceremonies may feel uncomfortable at times.