If you're going to the southwest to see the Grand Canyon, then you should see Chaco Canyon in northwest NM and Mesa Verde in southwest CO. While you're in CO, go to Durango and ride the steam train between Durango and Silverton. The drive between Silverton and Ouray is incredible (but make sure your brakes and power train are in good order).
If you go to Chaco, there are no close-by parks - nearest is in Bloomfield NM. There is a campground in the park, but DO NOT, under ANY circumstance, take your Airstream. The road is 25 miles of terrible (but Chaco is worth it).
Just outside Mesa Verde is an excellent campground. Highly recommended.