Now offering FREE High-Speed Internet Access in ALL rooms. The La Quinta Inn-Cheyenne is just a mile from downtown, close to the Wyoming State Capitol and Cheyenne Frontier Days Fairgrounds, the world's largest outdoor rodeo. We are near the Wyoming Air National Guard Base and just two miles from F.E. Warren Air Force Base. Visit Terry Bison Ranch and the State Museum and Art Gallery. Stay here for events at the Civic Center and the Ikon Ice Center (miniature golf, laser tag, parties).