If you want to meet any HDC folks while passing through Alb or try to setup a 4WD run in the central mountain area, post something up on the HDC (High Desert Cruisers) section of MUD:
HDC Club Forum
I didn't see if you had a particular part of NM in mind. The majority of the HDC folks live in the Albuquerque/Santa Fe area so we spend a lot of our time in the Jemez (NW of Albuquerque) and Pecos (North and East of Santa FE) mountains. That would be the Santa Fe and Carson National Forests.
The Pecos area mountains are less accessible for motorized travel because a huge portion of it is wilderness but there are still plenty of places to camp and enjoy the scenery. There are plenty of trails in the wilderness areas that are great for hiking and backpacking.
The Jemez area mountains have a lot of Forest Service roads and even more opportunities for camping, driving, rock climbing, hiking. They don't seem to be as crowded because there is only a small wilderness area there which allows people to be more dispersed.
The mountains around Taos are nice but I've not spent much time there.
The mountains around Chama are also nice but again, not spent much time. I think there are some good wheeling opportunities around there.
May is the transition time between the lower elevations starting to warm up to the point they may be too warm for some and the higher elevations warming up but possibly still a little cool to be comfortable. Just be prepared for extreme temperatures at both ends of the spectrum and you'll be fine.
If you're looking to visit some Indian archeological sites, there are many great ones all over the state, but most are within a couple hours drive from Albuquerque:
Chaco, Bandelier, Salinas missions, Acoma, Taos, Aztec ruins,
If you can spare the time, I'd also recommend Mesa Verde. It's in SW Colorado but very close to NM. If you go to Chaco, it's worth making a trip up to Mesa Verde as it's only about a 3-4 hour drive from Chaco.
It really depends on what you want to do.
