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... :-)
I-10 east of Benson, AZ - you absolutely have to stop in the Stuckey’s and see The Thing! Man or myth, alien or freak of nature - who’s to say?!