Hey ctb, you'r coming into my backyard!
So, you've got to check out Silver City. If you come by I-25 from Albuquerque, use NM152. It will take you over the Black Range through Hillsborough and Kingston. A longer but more adventurous way would be US60 from Socorro to Datil (visit the VLA and camp at Datil Wells) then NM12 through Reserve (camp at Apache Creek) and then US180 to Silver. There are many FS roads into the Gila along this route. If you want 4WD adventure take NM52 (dirt) south from US60 through Dusty then NM59 to near Beaverhead and FR150 south to the Mimbres Valley and NM35 to NM90. (Whew! better get a map!)
Checkout Silver City, WNMU Museum, SC Museum, downtown SC. Only GOOD place to stay is the KOA (owned it for 20 years!). Then from there you can checkout the Gila Cliff Dwellings (good camping), the City of Rocks (good camping), Faywood Hotsprings (OK camping).
In SE AZ you've got Cochise Stronghold (good camping), Chirichua NM (good camping), Ft. Bowie and (if you get this far west, Roosevelt Lake (my favorite!).
If you want to travel north when you leave, travel up US191 from Morenci through Alpine. Great boondock camping all the way.
I find it a pain to upload photos but you'll find many in our blog http://www.travelsofthemercury.blogspot.com
. If you need more info, PM me!