Used to live in Flagstaff. It's worth the trip but a few things to be aware of.
First, that area does get winter conditions (high winds, below freezing temps, possible snow), so make sure you keep an eye on the weather and have cold weather gear with you.
The highway is decent but is two lane. Second, check out the monument web site (
https://www.nps.gov/cach/index.htm) and see what's available. I don't remember what's available for campgrounds in the area, but the monument staff should be able to make suggestions (give them a call or email).
Also, be aware the monument is on Navajo land and you will be traveling through the reservation.
A few other spots you might consider stopping at would be:
Page, AZ (Slot Canyons, Glen Canyon Dam)
The Big Ditch (Grand Canyon)
Flagstaff (Lowell Observatory, Walnut Canyon National Monument, Sunset Crater NM (there is a US Forest Service campground across from the visitor center) , Waputki NM and more).
About 50 miles east at Winslow on I-40 is Homolovi State Park (
https://azstateparks.com/homolovi) - full hookups, ancient Hopi ruins. North of the park is Hopi. You can get excellent blue taco at the Hopi Cultural Center in Second Mesa (
Hopi Cultural Center).
About 2 hours east of Flagstaff - Petrified Forest
Another site you might consider is the Hubble Trading Post, run by the National Park Service (
https://www.nps.gov/hutr/index.htm). You can purchase Navajo blankets and other native art works.
I can give you some other spots to visit if you're interested.