Things to see, along the way (north or south of the I-40 line...)
Graceland - Memphis, TN
OK City Bombing - OK City, OK
Groom Cross - Groom, TX [huge cross on I-40, east of Amarillo]]
Cadillac Ranch - Amarillo, TX [west of city, next to I-40]
Roswell - Roswell, NM [swing south and see UFO museum... :=) ...]
White Sands National Monument - White Sands Missile Range, NM [if you do swing south to Roswell]
Four Corners - NM, AZ, CO, UT all meet here [if you swing north...]
Monument Valley - AZ, UT [if you swing north; you’ve seen it in all the westerns...]
Winslow Crater - Winslow AZ [about 20 miles west of Winslow on I-40]
Grand Canyon - AZ
If you do trips like me, you’ll be zigging and zagging and never making a straight line... LOL...
But, I see someone mentioned Carlsbad Caverns. And yes, by all means, if you can do the zigging and zagging, do see that one, for sure.
Another thing to keep in mind about the “time of the year” — a lot of places will be closed during that time of the year. It would definitely be better to do it late Spring or early summer. Check the times for places to open up again, being that many will be closed for the winter.
And so, in light of that, if you can zig/zag up to Mesa Verde (in CO), do that one, too... :-)