I think it's true that New Mexico often gets overlooked on westward roadtrips. It seems that the routes people go either go north through the Badlands and Yellowstone through Colorado, or just right from Texas to Arizona and toward LA.
Admittedly my first 6 week roadtrip totally bypassed New Mexico. In fact, we hit every state around it, but never actually went through it. The next summer, I lived there for a month, and this past fall, I made a point to go back, even repeating some locations I had already been to.
Now, out of the 31 states I've been to, it's my favorite one! It's a perfect pairing of Alpine mountains and desert canyons which offers tons of variety for outdoor activities! Not to mention the abundance of whimsical small towns, roadside stops, and culture makes even a day trip through the state one to remember.
I've briefly outlined some of my favorite places I've been to in New Mexico, which of course does not include all that the 47th state has to offer, but may be enough to inspire your next visit or your first!
Classical Gas Museum
Johnny's roadside collection of antiques and memorabilia from a long gone era.
Bandelier
A premier cultural site in New Mexico and just under an hour away from Santa Fe.
Carlsbad Caverns National Park
A massive cave system with a self guided tour featuring fantastic limestone structures.
Taos
A small town in Northern New Mexico with an eclectic artistic vibe.
Bisti Badlands
A remote and bizarre wilderness 36 miles south of Farmington
Diablo Canyon
A free BLM campsite and short day hike through a fabulous canyon
Dwan Light Sanctuary
A spiritual space designed with glass prisms which decorate the stark walls with light refractions
Kasha Katuwe
A site with 2 short hikes featuring scenic cone shaped formations
White Sands National Park
The largest area of sparkling gypsum dunes in the world.
Again, New Mexico has tons more spots and trails to offer, do your own exploring! These spots should provide a good starting point!