In Grand Canyon National Park, a nice four day hike across the canyon, the South Kaibab Trail as it drops quickly from Yaki Point to the Colorado River, 6.4 miles and 4,780 feet below (hike from Yaki Point a mile and a half down to Cedar Ridge and back for a good day hike). Spend two nights at Bright Angel Campground, just above the rivers north bank, with a day in between to explore the arduous Clear Creek Trail. On day three, pick up the 14.2-mile-long North Kaibab Trail and take it halfway up to Ribbon Falls and the Cottonwood Campground. A final seven-mile push lands you on the North Rim. FYI - there is no water on the South Kaibab Trail.
Overall, South and North Kaibab Trails is the 2nd most popular hiking trail of all 49 hikes in Arizona.