I did this three years ago on a family vacation at FLG. Wiseman Aviation had a couple of 172s. My rental checkout was very straight forward, but they knew I was a CFI and USAF T-6 Instructor Pilot. Out to practice area for steep turns, power on and power off stalls, back to the field for a short field, soft field and normal landing. It was quite an eye opening experience to have to lean for taxi, and then lean some more for takeoff.
We took off with half tanks, and 4 people, my wife, 9yr old daughter, and another female family friend on a 55 degree sunny October morning. I did a short field to get airborne, then accelerated to normal climb speed while still over concrete taking off to the north, but kept the flaps at 10 for a long time until we were at a safe altitude. Lots of tall pine trees surrounding the airport and not a lot of margin for error. It would have been nice, if they had something more capable like a 182.
After getting out of FLG, the flight was wonderful. We did not stop at GCN, but flew to GCN, then along the edge of the SFAR at 11,500 to the east and landed at PGA. We had a great view of the canyon from that vantage point. We added fuel at PGA for the rest of the day which was easy since the field elevation was a lot lower than FLG, and the terrain was flatter and takeoff much safer. We then went to Monument Valley and landed at UT25 and spent a few hours wandering the museum and eating lunch at Goulding's Trading Post. From there we departed and flew around the rock formations in the valley before heading back to FLG. I only wish we had time to fly over Sedona, but otherwise it rates as one of the best things I have ever done in GA.
I had a pre iPad portable GPS and carried survival gear, water and had a portable ELT with us from our own airplane.
Wiseman Aviation
http://www.gouldings.com/more/airport-information/