Personally I enjoyed the road direct from Cortez, CO to Bluff, UT - A combination of Montezuma County Road G, Ismay Trading Post Road in San Juan County UT and UT-162 from Aneth to Bluff, then 191/163 down to Monument Valley. It is a good route with almost no traffic. Made for nice easy towing and is about 30 miles shorter than the other route.
But we had already visited Four Corners Monument on a day trip.
The fee is $20 per day for vehicles with four or fewer people to enter the Monument Valley area - CASH only. The View Campground dry camping was listed as $40 per night in late October - CASH only. (Note - Mounument Valley and The View campground are actually in Arizona, but the entrance road starts in Utah.)
We chose to dry camp for $10 per night at Goosenecks State Park. That also put us in position to see the very similar, very wonderful rock formations at Valley of the Gods.
Our route to Zion then went up to near Blanding, across UT-95 to Capitol Reef NP. Then we backtracked to Arches/ Moab and over to Great Basin NP before back to Zion.
Our route across UT was because of the dates/ reservations we were able to get for Devil's Garden at Arches, and Watchman at Zion.
We plan to hit the lower end of Lake Powell and hopefully the North Rim in late April when we go from Tucson to Portland, OR.