Some of these have already been mentioned but I'll give you my ranking on a scale of 1 to 10 from the perspective of a "local" to the AZ portion of Rt 66 (I-40).
- Petrified Forest (6). Very scenic.
- Meteor Crater (4). Interesting hole in the ground. Kinda expensive but if you're in to the geology thing it's pretty cool.
- Walnut Canyon National Monument (6). Indian cliff dwellings and a nice hike.
- If you're going to the Grand Canyon (10) take N Hwy 89 to the East entrance. Less crowded entry point and it is much more scenic way to come in to the Canyon. Just North of Flagstaff off of Hwy 89 you can take a short loop drive in to Wapatki National Monument (6) and Sunset Crater National Monument. Extensive indian ruins. Lava flows.
- Stop in to the Cameron Trading Post (5). Have a Navajo Taco for lunch. AMAZING indian jewlery (See the copper and turquoise jewlery for a more affordable yet very beautiful). Check out the dinosaur tracks in the sandstone slab at the front door.
- After coming in to the Grand Canyon (did I mention that this is a 10?) East entrance you'll want to stop in at the several overlooks that you'll come to. Don't miss Lipan Point (10). You'll probably want to stay at the Trailer Village Campground. There is a free shuttle/tour bus that will pick you up and drop you off right at the campground.
-When you leave GC you're going to head South on Hwy 64. Take the drive on Hwy 180 in to Flagstaff and stop at the Museum of Northern Arizona (8). Route 66 runs through the middle of Flagstaff. If you spend a day or so in Flagstaff you can take a day trip down Hwy 89A to Sedona through Oak Creek Canyon (9). There is a pretty nice US Forest Service campground in the canyon. Depending on your rig it can be a challenge driving down the switchbacks.
- Just East of Williams on I-40 is The Deer Farm
(The kids will call this an 8 or a 9). My daughter was pretty sure that this is where Bambi lives.
- You'll get back on Route 66 at Seligman. There is a roadside buger/ice cream stop called Delgadillos Sno Cap (5). Very much worth the stop for a snack and a show. If there is a tour bus parked in front just keep on rolling.
- The portion of Rt 66 from Seligman in to Kingman is really nice. The Grand Canyon Caverns are pretty cool (6).
- To stay on the Rt 66 plan you're going to take the road up in to Oatman (6). Funky. Cool. Full of wild burros. When you roll West out of Oatman you'll end up at Topock (I-40) and the Colorado River. Just across the California state line is Park Moabi (5). There is a large RV park and a really good restaurant that site right on the rivers edge.