When I was in the military I made a number of coast to coast trips. Just ran the total and it totals ~ 16,000 miles. Great memories in my old Datsun 240z.
I totally agree with the advice and items Terminator and Epdarks have given. I'd add
Ensure you have a working jack, and tools to remove the wheels.
If have the space and the inclination I always put my garage light weight floor jack in for long trips. Haven't had to use it, but...
A tire puncture repair kit (with the pump Terminator recommend) can make short work of a nail puncture.
One of the portable jump start units can cover your emergency power, portable pump needs.

Tunes! When I was doing my travels the I had to use this thing called a "cassette" player. If you go to a museum you can find one. Just make sure you have music, as radio coverage will be spotty and anoying.

Finally, I know that Carlsbad Caverns is 200miles past Clovis but if you can, make the effort. On one of my trips I camped there to watch the bats leave. It was an experience I've never forgotten.

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2003 X5 4.6is Estoril Blue
2005 Infiniti G35X
1972 Datsun 240Z
1991 Isuzu Impulse XS Sold
1972 Fiat 850 Spyder Donated
1972 Datsun 240Z Sold
1972 Datsun 510 Sold