Our primary objective was to visit the Trinity Site on the Whie Sands Missle Range Open House Oct. 04, 2012, but we ended up making a big loop through NM.  

Betty and I have always been interested in WWII, and the Manhattan Project.
We have visited Los Alamos and Oak Ridge museums and wanted to see the 
Trinity Site.
We assumed the site wold not be very popular since it has limited access (see 
below) and we didn't think many folks would be interested.

We spent the first night at Alamagordo NM, the next morning we went to Tularosa.
We entered White Sands with a caravan which originated in the Tularosa high 
school parking lot.
The caravan was escorted by numerous Military Police vehicles.
Our fist clue, I counted the number of cars in the caravan about 175.
When we arrived we were further surprised, there were hundreds of people there.
I note that today the caravan is limited to 125 vehicles. 

After our visit, we drove north to the White Sands Stallion Gate, and then west
to San Antonio NM., and north to Albequerque where we spent the night. 

Just the existence and location of this National Monument is interesting:
The Trinity Site is almost in the center of the White Sands Missle Range (White 
Sands Bombing Range during WWII), a highly secret and heavily guarded military 
base.
It is only open, the the public, two days per year, for about 6 hours each.
Please see the Trinity Site Open House site