After looking at the map in your link, I'll throw in some suggestions for your consideration:
After Amarillo, head southwest to
Carlsbad Caverns National park. The largest and best decorated cave we have ever visited.
Between Grants and El Morro, you will pass through
El Malpias National Monument,with lots of easily visible lava flows. We stopped at the
Bandera Volcano & Ice Cave. It's on private land with an entrance fee, but they have a short trail to a collapsed lava tube with perpetual ice at the bottom and a longer trail to look into the crater of the volcano.
For the Petrified Forest, we stayed at the KOA in Holbrook.
A short distance west of Winslow, is the
Meteor Crater.From Flagstaff, consider taking routes 89 and 64 to the South Rim. This will allow you to take the side loop through
Sunset Crater Volcano National Monument and
Wupatki National Monument.Route 89 between the junction with route 89A and page has been closed since February due to a landslide. Keep and eye on this
AZ DOT website for updates on the interim detour route. If you don't need to go to Page, you can take route 89A to get to Zion.
After Zion, I strongly recommend heading north on route 89 to
Bryce Canyon National park. Absolutely breath taking scenery.
From Bryce, you can continue up route 89 to join I70, or, if you are a bit more daring, take
route 12 to Torrey, one of the best scenic drives we have ever taken (actually we drove it twice). From Torrey, route 24 passes through
Capital Reef National park and past
Goblin Valley State Park before joining I70 west of Green River.
On the way home in Hays, Kansas, a short way off the Interstate is
Fort Hays Historic Site.
