@ZombieCat pretty much nailed it, but i'll throw in my take on new mexico since it is one of my favorite states to visit...
first off, i'd go on amazon and order the DeLorme atlas and gazetteer for new mexico
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lots of great info and in the upcoming months, you can get advice on places to see and reference the gazetteer for location and more info.
time and money will be a determining factor on how you plan the trip and there are basically two ways to approach the trip: find specific things you want to see and concentrate on that area OR do a recon trip to see as much as possible with the idea of seeing all you can see and then in the future, plan a trip for specific areas that caught your interest on the recon trip. it is a big state and a lot of things are pretty spread out...
if you are coming in on I-40, angle up to santa fe and check that out. amazing place with a lot of sites and art studios if you like that. from there, go up to taos and you can make a circle going up to eagles nest and red river. VERY scenic and there are camp grounds. if you are digging the southwest vibe, then head northwest from taos to shiprock. there is BLM land and some nice remote camping west of taos. as you go further to shiprock, you will see the cool scenery like in the coyote and roadrunner cartoons with big rocks perched on top of eroded peaks and all the red and tan colors of the mesas. shiprock is cool and that puts you close to mesa verde cliff dwellings like zombiecat mentioned. a very unique area and worth it just to drive thru it.
depending on time, you can drop south on 491 from shiprock and hit gallup which will put you on I-40 if you are heading home and need to make time.
if not...then you can stop in albuquerque and check that out and then drop down on I-25 to las cruses and then north on 70 to see white sands national park and up to alamogordo and thru cloudcroft which is very scenic and head west to artesia and then drop down to carlsbad caverns. i've been there a dozen times and still love going. there is BLM land all around there and we've desert camped outside of carlsbad and enjoyed the remoteness and the wide open skies at night. from there, you can either angle your way back up north thru roswell and hit I-40 or drop down from carlsbad and hit I-10 and shoot across the soul sucking barren wasteland of west texas and hit san antonio and check out the riverwalk and alamo and then work your way back northeast or continue on I-10 thru new orleans and check that out and travel the gulf coast working your way northeast as you go.
get the gazetteer and watch youtube vids on people traveling new mexico and you will get a good idea of what all is there and what would be of the most interest to you.