It's not quite a hike, but you can take an aerial tramway to the top of Sandia Peak (within Albuquerque), which is something like 10,000 ft elevation, and see the city and desert for many miles around. I was there at a time of year (don't remember when, I'm afraid) when there were small local thunderstorms wandering about the desert, which was very interesting and unique to see from the mountaintop. (I haven't spent more than a couple of days there, though, other than on business, so I don't know what else there is.)
Santa Fe is about an hour away, too, and it has some historic architecture and atmosphere.
Lisa