Just outside of Gallup is a Navajo Chapter House called Church Rock. The "rock" itself is in its own park just off Highway 666. To reach the top takes about an hour, if you've been there before, and about two hours to the average tourist.
The web site I list just show a picture of it and a brief description.
Note: You do not have to be a trained rock climber to enjoy Church Rock.
Fantastic Navajo rugs for great prices. This is held in Crownpoint NM, it is attended by many dealers, so get there early so you can look over the rugs before they are auctioned. They auction hundreds of rugs each night it is held and it goes fast!
Most importantly, the sale price of the rug goes right to the weaver the night of the auction. You might get to meet the weaver of your rug.
Bisti De Na Zin Wilderness area is about 2 hours from Gallup. It has petrified logs, dinosaur bones, surreal landscaping, and is just in the middle of nowhere (that's a good thing).
All I can say is if you like strange rock formations then you must visit this area. Bring water and food because there isn't anything around there where you can get it.
I read somewhere that this area was a possiblity for filming "Star Wars", you'll know why once you get there. To get there from Gallup you take I-40 East to Thoreau and then take Route 371 North past Chaco Canyon and past Crownpoint to the small sign that says Bisti Wilderness.
It's about 4 miles on a dirt road to the parking lot and you have to hike at least a mile befor you'll see anything really different but it's almost as if there is a gateway into the badlands and once you hit it, you'll know. Follow the wash from the parking lot to get there.