OK my first thoughts. I assume you've seen the eastern NP. So you aren't going to hit major parks until you get to New Mexico or Colorado on a southern/central route. Now You can take I-40 west all the way into northern NM. If you want to see Carlsbad Caverns, which are well worth the trip, then get on I-30 off I-40 to I-20. There is a good large NP in southwest Texas, Big Bend, but it's best in the cooler months.
There a number of National Parks and Monuments in New Mexico, mostly smaller parks that you could visit. If you go to Carlsbad and take I-25 north to I-40 again then west from there.Santa Fe is a frequent tourist stop as is Taos. You can visit some live Indian Pueblos in the area.
Instead of taking I-40 West you could continue up into southern Colorado and take US 160 west which will run you thru spectacular mountain country. Follow 160 west past Mesa Verde NP. And continue on thru Cortez CO where there are a number of various parks in the area. Monument Valley for one but there are 7 or 8 others.
Following US 160 down into AZ and then south to the south rim of the Grand Canyon. Back on I-40 to Kingman and then northwest on US 93 to Vegas. Then the suggestion to Death Valley is good and follow 395 north.
You can then either divert onto 120 to go thru Yosemite NP. Or go passed there and there are a number of roads heading west which will bring you to Alameda. Including way north is I-80.
I think you will find CA much the worse for wear from the last time you saw it. Be prepared for major potholes and outrageous fuel prices. The roads are in awful condition, 395 last time I was on it a few years ago was an exception.
You need to get a map and get on nps.gov and think about where you want to go. That will form your route for you. Ask more questions as they come up.
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