Living in the subject area, my advice is to fly early when the lighting is best and the air is smoothest. Flying over in the afternoon at 14k will cause you to miss the sights and the beauty. With good, early morning light, the colors come alive!
If not familiar with the effect of density altitude, please brush up. Most of the ground in this area is higher than the typical pilot cruises. Takeoff and landing at 11,000' DA is different. Cruising at 8,000' and skimming the ground is unnerving if not prepared.
Watch the winds aloft at 18k. That will tell you how rough it will be over the mountains. If the winds at that altitude are high (40kts), expect rough.
Depending on what you want to see and do, the whole area is a huge playground. Monument valley is neat but, sadly, it is a tiny little place (when going 150 kts). Be sure to see Canyonlands, Bryce Canyon (you can land at the airport and get a shuttle to the park to walk the canyon trail), Comb Ridge, Goosenecks, Capital Reef, Meteor Crater, Gila Wilderness area, etc.
If I were flying CNM to PGA and the weather/winds aloft are good, I'd fly west towards LRU to get around White Sands to the south. Then head direct to PGA or Monument Valley. This will take you over the continental divide and some great sights. If you want to see the lava flows and chain of craters, head towards GNT. If you want to see Shiprock, LRU direct to 5V5.
Another great option (for sights) is LRU to JTC (Springerville) to SEZ (Sedona) and then to PGA. There are also some really great backcountry strips available if looking to camp or do that kind of sightseeing.
The only real problem is that this is a MASSIVE area making it hard to see it all in one trip!