I recommend planning on driving around for several weeks (it is the 3rd largest state in the union).

If you are coming from the west, stop at El Moro near Grants off I-40, there are some Anazazi ruins at the top of the mesa as well as a cool oaisi with poetry and messages written by conquistadores and priest on their way north from Mexico City and sout back.

More Anazazi ruins at Chaco Canyon, Aztec, Farmington (Mesa Verde 2 hours north of Aztec)

Albuquerque Sandia mountains has the longest, highest tram in the U.S. The view is amazing. It goes from the west face of the mountains to the peak, about 11,000 ft above sea level.

Santa Fe is fun, and there are art galleries all over, no matter what town you visit.

Also on the way to Chaco from Albuquerque there is a turnoff to Jemez springs.

Southern New Mexico has White Sands national monument, Carlsbad caverns, and something near Deming (can't remember what).

If you wait until July Roswell has a UFO celebration that is a hoot. If you are in that area there is a strange place called Bottomless Lakes that I think everyone should see.. And in the summer on the road between Vaughn and Clines Corners you can see the tarantulas cross the road in droves just before dusk. (there is a ranch that has Oryx near the highway too)

Lots more, but my brain is too tired to remember it right now.

I love living here. A lot of folks however mainly in high school or just getting out of school want to move on but most end up coming back at some point. There's lots to do but you need to get out and look for it. With a half tank of gas you can completely change your surroundings.