Graywolf likes, as one of the best hikes in the world, the Thunder River/Deer Creek Loop in the Grand Canyon:
It is a very demanding and beautiful 26 to 43 (w/side trips) mile hike from the North Rim to the river and back. Awesome scenery, beautiful river, creeks, and falls and a wonderful play area in the Deer Creek narrows. To enjoy the fullest, plan on 5 night/6 day trip which would include a layover day in Deer Creek.
Start from the north rim on the Thunder River Trail, descending about 4600′ (1400m) to the Colorado.
Return to the north rim via the Deer Creek Trail.
This hike is strenuous and can be dangerous: severe weather, over-exertion, dehydration. Even flash flood. Desert hiking experience essential.
No need to carry canyon climbing gear — though you can use it if you do.
Deer Creek Narrows – larger original – flickr
Mike Miles posted a most entertaining trip report – Hiking Grand Canyon; an adventure on the Bill Hall, Thunder River and Deer Creek trails. They were physically challenged, injured and bothered by a marauding ring-trail cat.
Colorado River mile 134 beach camp
We’ve added the Thunder River/Deer Creek Loop to our list of the best hikes in North America.
besthike.com 
Woah, that looks brilliant!