Looking at the post by Bussdriver, I would second it.Come into New Mexico and make sure that you hit Chaco Canyon. The other that I would prefer is to do it by coming across Wyoming to Salt Lake and then south to Zion,up to Bryce and camping at either the private one there or N.P.,over to Kodak state Park, Capital Reef N.M camping at Fruita CG. Then up to Goblin Valley SP, down to Natural Bridges NM, camping there. After that would be Monument Valley,Canyon De Chelley, over to Chaco Canyon. From there back over to 4 Corners and up to Moab and Arches Then home over I-70.
Hoping that you have a toad of somekind as there are lot's of places where there are LARGE areas to explore. I did that in my '94 Cherokee and my two person hiking tent. Only had snow,10" of powder snow at Bryce but temp was 10 degrees that night. As said before prepare for temps up into the 60s-70s during the day and down as low as 10 at night at evlevation.
Have an awesome trip.