My favorites are listed below. We can only go in December/January, so my choices are limited to lower altitude areas where the weather seems pretty reliable. E.g. to me Texas seems to be variable and I've never been able to hit the weather right.:
- Catalina State Park, AZ (good hiking and biking, basically in town but you can't tell. Sonoran Desert museum and Sugaro national monument.)
- City of Rocks, NM
- Dead Horse Ranch State Park, AZ (Near native ruins, Prescott, and Jerome mining town)
- Kartchner Caverns State Park, AZ (amazing caverns and a little bit of good hiking)
- Organ Pipe Nat. Mon., AZ
We transition from winter to summer at Coronado Campground in Bernalillo, NM. I like that a lot because of the Albuquerque bike trail. I think the trail is called Del Bosque. Sante Fe has a couple of RV parks if you want to see the museums.
Lost Dutchman is okay if you need to be near a city to provision or if there is bad weather. Nice hiking but the glow, air pollution and sound of Phoenix.
If you can go a little bit later, I would strongly recommend the Chiricahuas. I am nervous about the stream crossing at the Cochise Stronghold, so I would stay away from that. Go to the eastern monument.