JCat, We try to get from home to St George the first day some days we'll stop at Oasis RV Resort in Vegas. About 10 miles north of St G is the turn to Zion via Hwy 9. Zion is not one of our favorites and everything has been crowded when we visited. Driving through was the best part of being there. I don't remember the height restriction for the tunnel but at 11'6" we fit.
Continue on 9 to 89 to 12 to Bryce Canyon NP. Technically Bruce Canyon is not a Canyon but it is spectacular. We have been in the winter, spring and summer, doesn't matter the time of year it's going to be fantastic. You really need time to explore in the early morning and late afternoon to appreciate the colors and forms.
I would take 12 to 24, east on 24 to Capitol Reef, it can be very crowded. We couldn't get in the last time we were there so it's been a long, long time since we explored CR. I don't remember it at all.
Hanksville and then South on 95 to 191 and then North to Blanding. The last time we were there we stayed in a Campground behind a trading post on the West side of the Hwy. Nothing special but we used the campground for a base that covered, Natural Bridges, Moki Dugway, Muley Point, Goosenecks and Valley of the Gods. We visited all five in one day. Don't do that! Split is up anyway you want, I would do Natural Bridges, one day and maybe Muley Point. It's a long drive to do all five sites. There is dispersed camping In Valley of the Gods and while it is possible to take a large Class A down there I wouldn't unless you are all very skilled in steep switchback dirt roads.
The needles District of Canyonlands is worth the drive, you can make it in almost any passenger vehicle from Monticello to the Visitors center but there isn't a lot of camping so I'd stay in Blanding or Monticello.
There is camping in the Northern district, Island in the Sky and at the State park at Dead Horse point. I took my little Sidekick down into the area below Dead Horse Point from the Visitors Center at the entrance to Island in the Sky. No sedans when we were there. Dead Horse Point is a great overlook into the canyon.
Just North of the turn off for Dead Horse Point and Island is Arches. The road has been known to be closed due to the high volume of visitors and camping is at a premium. Campground reservations in all five parks are necessary.
Actually I would go to the Visitors Center in Monticello before doing much exploring around the Southeast part of the state. You may not know what a Dugway is, I know I didn't know there was a name for roads like that. You can find out that and much more at the visitors center.
Another interesting thing to do is drive up the Colorado River Road from N/O Moab and S/O Arches as far as you care. It is very different than other parts of the river.