If you are considering Mexico check out Mata Ortiz and Casas Grandes. Only a few hours from Douglas AZ or Columbus NM. Interesting stuff and on the way to Barrance del Cobre or at least on one of the ways to Copper Canyon.
If you are considering the Copper Canyon area these guys are a wealth of information, they worked with me before we headed to Mexico by email and again once we were in Creel. Gave us advice on where to stay, what to do, how to get there, maps etc. I asked what we owed them and they just asked that we pass along their name. http://www.amigos3.com