Thanks everyone. I have to ask you more questions!
My friends have come up with two more suggestions. One is Sedona, and the other is the Navajo reservation that Tony Hillerman wrote all his books about and that has some big canyons. Is that area too far north for warm weather?
Navajo country is too far north and too high up for a warm winter break. But if you bring a warm jacket, it will be magical that time of year. Sedona will be nice, but with cooler days so that you'll need a light jacket (but not cold enough for your winter gear). Nights are nippy in Sedona.
If you want warm weather, Phoenix area is nice. I personally enjoy Flagstaff more, largely because of the beautiful Sequoia cactus forest that surrounds it.