Desert SW trip advice, please.

There is a sign at the entrance to tour monument valley that says "NO RVs".

Just mention that you are a truck with some cargo and in you go.

Meteor Crater is not worth the entrance fee. There is better stuff around Flagstaff.

When I would recommend North Rim - the roads are closed for several months each winter.
You can boondock outside the park for free as this is perfectly legal in AZ.
If you like the thrill- go for Sky Walk.
Monument Valley is gorgeous and I drove the loop with TC on it.
I think I stretched the ordinance, but nobody stop me.
They have big parking lot, where you can leave camper and take a loop with truck.
The Valley Campground is very basic, so don't plan for luxury.
Mexican Hat in UT is worth stopping for pictures if you are not far away.
And my all-time favorite Lake Powell with all the Antelope Canyon, Rainbow Bridge, Horseshoe Bend and more.

Meteor Crater would be last on my list. Monument Valley with a guided tour would be at the top of the list. From Monument Valley you could go to the South Rim if north is still closed.

Two Hands wrote:
For boon docking you’ll probably want the north rim as opposed to the south rim of the Grand Canyon.

The North Rim opens late and closes early due to high altitude.

Check out Campendium and Free Camping

Nice Boondocking west of Flagstaff at the entrance to the Naval Observatory.

Free Camping at the lake at Winslow AZ where you can take it easy waiting on a corner for a girl in a red truck

I would skip meteor crater and add walnut canyon near flagstaff. By Late March early April you should be through with the worst of winter but there is always a chance of a storm even up in May. Just watch the weather forecast and even in Jan you may have weeks with sunny sky's and fairly warm weather. A lot depends on the elevation and where you mentioned is at higher elevations vs the low desert around Tucson. You might consider day trips to the higher regions and stay lower down in the evenings. Remember you can get 45 degree difference between night and day in the high desert.

PS north rim is closed from Oct to May

For boon docking you’ll probably want the north rim as opposed to the south rim of the Grand Canyon.