You mentioned the North Rim of the Grand Canyon. Toroweap is accessed by 60 miles of dirt/sand and gives you access to one of the narrowest parts of the canyon above Lava Falls, 2,800ft straight down. We could hear people talking on the rafts as they approached Lava Falls. Now days, you may need a permit, although I'm not certain. Camping is allowed. 18 years ago in July there was hardly anyone in there, camping was free and we never saw a ranger. I believe those days are gone. Well worth the drive, as long as it's not wet.
In Utah, The "Little Grand Canyon" or San Rafael Swell. Remote but spectacular scenery. Campground with pit toilet but no water or other amenities. Went through there in mid September and no one was there. Of course, that was then and this is now. The overlanding thing has exploded, add in the pandemic factor and finding lonesome places is more challenging.