People drive through on I-40, think they've seen New Mexico.
We're I a stranger wanting to explore on wheels, I'd drive all the forest roads in all the mountains I could each day, then find good eats in the small towns at night, have a beer, talk to the locals.
If you like architecture and history, just finding really cool old churches could be a thing, without even bothering with the big, well-known ones. Also some cool Pueblo ruins scattered about.
Where New Mexico truly shines is off the beaten path.