So many choices in Northern AZ and Southern UT! In my humble opinion, 6-7 days may seem like a lot of time, but with the ground you're hoping to cover/see, you'll likely only check off a fraction of the items on your list. My recommendation would be to focus on two areas at most, and try to get the most out of each while considering travel time in between.
Since you'll be starting in Flagstaff, I'd recommend the
North Rim Grand Canyon, which has a fraction of the crowds compared to the south rim, along with some absolutely exquisite and awe inspiring viewpoints and campsites. You could easily spend 2-3 days exploring from the North Rim Visitor Center working your way up to Freedonia and then continuing on through Utah. Most of the roads are relatively non-technical in nature, so you should be fine.
I've gone ahead and listed some other options that we have for published routes on the site that may interest you. My recommendation would be to read through each one and see what pique's your interest. Lots of options to bail part way through a route and continue on your way. I'd also recommend looking into Capitol Reef. We've been sitting on a Cap Reef route for sometime, and we'll probably publish it next year. If you're looking to get away from the crowds of Moab, Cap Reef is probably a good option as long as the weather holds up. Happy to make some route recommendations and POIs to check out along the way if it seems of interest to you.
Since you're looking at starting near Flagstaff, you might consider doing half of the
Sedona Backcountry Trail, specifically the section starting from Kachina Village. The viewpoints of Sedona are second to none and you can easily shoot north to I-40. Just keep in mind that you'll see a lot more people on the trail than the North Rim.
I'd also recommend checking out the
Cedar Mesa Heritage Trail, that basically runs from Moab through Bears Ears NM and down to the Valley of Gods. You'll want to skip the Elephant Hill section as it's pretty technical up there. You could start from the south and once you hit Blanding, skip the rest of the trail.
White Rim trail is always a popular one in moab, you'll just need to secure your camping permits in advance as they can be difficult to come by. Expect
a lot of trail traffic (4x4s, mountain bikers, and hikers) throughout the route.
