The hike from one side of the canyon to the other is known to be the best in the USA. You can walk from the South Rim to the North Rim or the other way around. It will take a couple of days to walk the total route of over 30 kilometers/18.6 miles.
It is best to do this with a guide and to spend the nights in tents. This is the ideal way to absorb this natural wonder.
More information: www.justroughinit.com