Lots of good suggestions there, so I'll just mention our trips around the West... Our purchase of the 718 Cayman S last August was hurried by anticipation of a September road trip from Washington to SW Colorado, a place we had not visited before. Moab UT was this trip's first glimpse of the dramatic red-rock country. Roads were not as well maintained in Utah as they smoothed out noticeably as soon as we crossed into Colorado through Cortez and Durango. And suddenly, lovely green forests! We stayed two weeks in Pagosa Springs, 50 miles east of Durango, and while there explored the area including a day trip to Taos, very interesting to see the deep canyon of the Rio Grande there, and of course the Taos Pueblo. From Pagosa, hwy 160 turns northward over the continental divide, with some great landscape views over the San Juan River valley, and switchbacks.
One of the more memorable drives was returning from a shopping trip to Farmington NM... heading east on 64 through Bloomfield we turned left just after Blanco onto 511, a twisty road past Navajo Dam. Just after the dam we encountered the only other traffic, a newer sedan. I don't know what kind, as I was concentrating on passing safely on this narrow and bumpy highway. He picked up speed to follow me and I put on some more speed. Due to visibility around corners, the undulating surface, and unfamiliarity, I didn't go full out, but I will say that ~70mph was plenty thrilling! He kept up all the way to Ignacio CO (again the road got a lot better after crossing into Colorado), so I was impressed with his skill in staying on the road.
I'll agree with the value of visiting Mesa Verde for the cultural/historical value of the native structures, and it's a one-way in and back out experience with major interest out where the road loops around the end. Pretty much the same for Bryce Canyon which has not been mentioned... I'd add that as a must-see. Here it's the fantastic red-rock formations around the ridge that one drives out on. Go first all the way to the south end of the road and putter around on the return.
We also passed through Monument Valley and I think we didn't do it justice by driving straight through, but it's spectacular. Four Corners is just a spot on the map in the middle of "nowhere", no other reason for interest IMO, and the structure there is simply a large group of souvenir stands operated by local tribes. And they charge admission!
Some years ago we spent a week in Oak Creek / Sedona, and I have to say I'm fond of it. Agree about the restful atmosphere there, as I was recuperating from a bruised rib at the time, and sat reading in the warm shade. There is one spot off the road up to the Sedona airport, a saddle between two mesas, that is said to have a spiritual nature... saw later that it was mentioned as such in an online search. Restful, and a calm place for meditation. Indeed when I visited this spot there was an East Indian gent in the lotus position on a comfy boulder meditating in the warm breeze overlooking the Oak Creek valley.
We'll be back in that area again this May with the Cayman, staying two weeks in Flagstaff, a good base for explorations I think. Already looking at the maps...

Back I think through Las Vegas, Pahrump, Tonopah, Lee Vining, and over the pass to Angels Camp...
Doug