If I have your location right from your thread on 3 weeks to go,you are in Amarillo and headed west .. on I-40 I assume.
It is hard to give you specific ideas when we don't know where you want to stop or what you want to see. If you have no interest in hanging in ABQ or Santa Fe and keep going, you'll get to signs for El Morro near Grants, NM. That is a Park Service site but I'm pretty sure they no longer charge fees for their campground. And there are some pretty neat lava flow things to see out there.
Don't forget, folks gave you several sites to look into for free campsites on your Free Campsites thread, too.
About camping anywhere on Forest Service or BLM... from my experience anywhere near Albuquerque, that is not quite true... like in the Sandia Mtns. I am not aware of any boondocking sites there. I was living in a sticks and bricks in the East Mountains for a few years. Maybe someone will know otherwise, but there is so much private land intersperced.. I never could find a spot anywhere around except Cracker Barrel and Walmart.