Road Trip MO to Grand Canyon???

I suggest staying in Williams and taking the train to the South Rim. Leave the driving to the engineer.
BTW unless you hike the average length of time at the South Rim is less than 3 hours!

You can get in some Route 66 aura by driving through the business route of I-40 in Tucumcarri and Santa Rosa. I would not try driving Central Ave in Albu the old route 66 route.

When you get to Grants and Gallup again take the business route for some 66 type sights and feel.

By turning south at Grants you can follow NM 53 to El Malpais and the Zuni reservation. From there you can go on over into AZ to US 191 or turn back up to Gallup on NM 602. I would go up 602 just to see the cliffs near Gallup and do some shopping in the old part of town.

Painted Desert and Petrified forest are worth a drive through and you can camp at Homilovi State Park near Winslow.

There is more old 66 driving in Holbrook and Winslow but the main old 66 route is west of Flagstaff at Ash Fork, to Seligman and over to Kingman and Oatman.

Amarillo Travel and Info Center across I-40 from the Flying J truck stop is a good spot to stop/boondock for the night. Secure, bathrooms, vending machines, and wifi. Haven't been there in about 6 years since we discovered it, but it gets good reviews.
Amarillo/Texas boondocking

There's also Winslow, AZ (think Eagles song "Take It Easy", might be worth a quick look, if you like that sort of thing). They have a Walmart for free overnighting.

and Meteor Crater, a little further west along I-40 (again if you like that sort of thing). We got there late in the day the last time through, and thought what the heck, let's go see what it's about. They were just closing up. Asked if they'd let us take a quick look for an "after 4 pm" price, but they wanted the full entry fee which was a bit pricey to look at a big hole in the ground, so we just kept going. Maybe some other time.

Flagstaff has 2 Walmarts for low cost overnighting and restocking supplies.

Just north of Williams, off I-40, there's a nice campground, "Kaibab Lake CG". It is right off of AZ-64 which is one of the access routes north to the South Rim of the Grand Canyon. Very nice spot.
Kaibab Lake CG

If you truly begin your trip from "Central Missouri" as opposed to "near Springfield" our preferred route is US-54 across Kansas, the OK panhandle, the TX panhandle and meets up with I-40 at Tucumcari, NM. This bypasses the two turnpikes in OK between MO state line and Oklahoma City on I-44.

Check out the freecampsites.net listings. There's a park by a lake with 4 campsites at Elk City OK, if that works with your travel times.

Are you retired? Traveling that distance for a couple days at the Grand Canyon is a long, expensive trip. I'd recommend planning for a month or two to visit the whole immediate area as long as you're there.

If you can add more time at least spend time in the southern Utah national parks - Zion, Bryce, Capitol Reef Arches, Canyonlands in addition to the Grand Canyon. You could also easily work in Monument Valley which isn't a national park but very pretty.

If you're 62+ you can purchase the national Senior Pass which will admit you to these wonderful parks free and give you 1/2 price on campsites. It can be used in national parks, national forests, national wildlife refuges and other public areas.

I-40 does pass through the Petrified Forest in Arizona, which is something you should see. It's a lovely drive through the desert with frequent stops along the way having short hikes to see interesting and beautiful examples of petrified specimens.

There is also a large knife store near Holbrook, AZ, directly across I-40 from a campground. The campground is nothing fancy, but it is inexpensive. I spent the night there a few years ago and full hookups cost me $20. Then I popped across the Interstate and spent a couple hours prowling the huge selection of blades. Wound up buying a nice folding ceramic-blade that is my daily-carry.