Cheyenne Regional Medical Center They are knowledgeable in the following conditions / disorders: Varicose Veins & Spider Veins. Cheyenne Regional Medical Center is located on 2301 House Ave Ste 203 in Cheyenne. They can be reached by phone by calling (307) 634-2273 . They can be reached by calling (307) 634-2273 . They have not yet been reviewed on MojoPages.com.