Great advice in here guys, thanks! Please keep it coming, can't have too much info on a trip like this.
Will continue revising my route and plan. Definitely will up my budget to $1,500, hit the spots you all suggested [Utah and Sedona], and pick up an air mattress as well. No speeding, got it
I originally planned to travel a bit more south, through Tennessee. Here are the POI I had in that route, not in any order:
• The Parthenon – Nashville, TN
• Blue Hole of Santa Rosa – Santa Rosa, NM
• Foamhenge – Natural Bridge, VA
• Grand Canyon National Park – AZ
• Meteor Crater – Winslow, AZ
• Petrified Forest National Park – AZ
• Slide Rock State Park – Sedona, AZ
• Great Smoky Mountains – Gatlinburg, TN
• Lost Sea Adventure – Sweetwater, TN
• Palo Duro Canyon – Canyon, TX
• Petit Jean Park – Morrilton, AK
• Petroglyph Monument – Albuquerque, NM
• Mojave National Preserve – Barstow, CA
• Forbidden Caverns – Sevierville, TN
• Burgess Falls State Park – Baxter, TN
• Luray Caverns – Luray, VA
• Natural Bridge Park – Natural Bridge, VA
• Shenandoah Caverns – Mount Jackson, VA
• Grand Caverns – Grottoes, VA
• Shelby Farms Park – Memphis, TN
• Appalachian Caverns – Blountville, TN
• Red Rock Canyon State Park – Hinton, OK
• Groom Cross – Groom, TX
Edit: Well, I guess as stated above, Rte 40 and 66 are recommended. TN would be a different route.