In June 1976 I hiked with my father and two fellow Boy Scout Troop 71 alumni, from the South Rim, down to the Colorado River (where the Bright Angel Campground was full, with no reservations available), halfway up the north side, and then east along the trail to Clear Creek, where we spent the night.
Our wilderness permit had "Not Recommended" written with a marking pen across the top in big, red letters.
Then we returned to the Bright Angel Campground for our second night, before leaving bright and early for our hike back up to the South Rim. It was fun having all the tourists staring at us as we hiked out with our backpacks, and was a good warm-up for my next three weeks in the Army Airborne School at Fort Benning, Georgia.
I cannot over emphasize the importance of having plenty of water for the hike back up. If you have an ambitious hiking agenda, perhaps it is best to save Monument Valley for another trip.
During my last trip to the Grand Canyon, where I bought my lifetime National Park Senior Pass, I stayed at the Spring Hill Suites in Flagstaff. But the crowds are much less in December.