Most of the UPS stores will accept US Mail as well. See the map in the link. I believe the one on the Flamingo might be your closest.
http://maps.google.com/maps?rls=com.microsoft:en-us&oe=UTF-8&startIndex=&startPage=1&um=1&ie=UTF-8&q=post+office+las+vegas+nevada&fb=1&gl=us&hq=post+office&hnear=0x80beb782a4f57dd1:0x3accd5e6d5b379a3,Las+Vegas,+NV&ei=BTdaT9nBMMPSiAKA4v3ICw&sa=X&oi=local_group&ct=image&ved=0CAgQtgM
()