In January I'd suggest staying on the I-10 route or secondary roads that follows the route somewhat.
If you have plenty of time, how about Big Bend National Park? Stay at Rio Grande Village in the park. There are full hookups and dry camping sites.
Carlsbad is a good stop. We stay at Brantley Lake State Park. Rent a 'wand' and as you walk in front of a particular formation or area it will talk to you - your own private tour.
White Sands Nat'l Monument in New Mexico is unique. Nearby Las Cruces has some fine Mexican dining.
Deming, NM has an excellent museum of 'everything'. We typically don't like museums but this one is great.
Stop in Benson, AZ for visiting Tombstone, Bisbee and Sierra Vistas great birding/hiking canyons. Ramsey Canyon sometimes gives tours. Definitely stay at the Saguaro Escapees RV Park in Benson. For a non-member, first time visit you can stay on an awesome full hookup site for $50/week. It's a friendly, active park.
Even if you visit Carlsbad it would be worthwhile to take the Kartchner Caverns tour near Benson. They are completely different. Kartchner is a living cave so still growing and dripping. The lighting is beautiful and the tours, great. (We gave them.)
Tucson is worth a stop - lots to do including a drive up to Mt. Lemmon, the Desert Museum, Saguaro Nat'l Park, Titan Museum, air museum, and awesome hiking.
How much time did you say you had?
.... probably not enough.