When I worked at Organ Pipe Cactus National Monument out in Southern Arizona (it is bordered on the south by Mexico) one of my most interesting hikes was to go around the base of a mountain in the Ajo range called Montezuma's Head that is free-standing from the Ajo range. You can hike around the base of it without having to climb any large ridges, and the route includes the old path of the Butterfield Stage Line that used to run through there from Tuscon through various old now-vanished ghost mining towns. There are lots of other search results if you're interested.