Colca Canyon, located in southern Peru, is one of the deepest canyons in the world, with a depth ranging from 1000 to 2000 meters. You can choose to do a day trip from Arequipa (which is a VERY long day with all the driving) but good if you are short on time...or you can do a one or two night trip hiking through the canyon and staying at accomodation along the way. There is some really beautiful homestays with pools and views to rest at.
This canyon is famous for Andean condor sightings so bring your camera!