There are many great long-distance bike routes across New Mexico. One is from Four Corners through the Mountains and it is truly grueling and yet spectacular up and down the mountainous terrain and such a ride is not for the amateurs, unless you are diehard of personal character. Then there is another lower route on Hwy 180, very scenic as well through Silver City, Hatch, White Sands, Ruidoso and into Roswell then into Texas. That is worth doing, no I have not cycled it, but I have taken that route by motor home, very nice.
Let us consider different and yet equally spectacular route. Lets start this Trek in Springer, AZ on Highway 60 at about 7000 feet above sea level. You will enjoy the 12-mile warm up as you approach the New Mexico Border. Riding across the high plain takes a lot out of you indeed.
Once you cross that border it is a good 32 miles until you even hit a major cross road and when you do it will Hwy 32 and it will be a two lane highway with a stop sign, but not for you, you need to keep riding for another mile or two and then you are in Omega, NM. Yes very nice folks there, but you need to keep riding, we have barely started and NM is a huge state to cross.
There will be many towns along the way some actually have names, but are very small. At about the 65-mile mark in the trek we will come to the Intersection of Hwy 12 and Hwy 60. No you will not be allowed to turn, you must keep going. At about the 95-mile mile marker we will see the VLA or Very Large Array, with the radio telescope antennas (seen in the Hollywood Movie; Contact). We will have dropped about 500 feet in elevation and soon start the 23 mile down hill journey into Socorro, NM at an elevation of 4600 feet.
This is a good days ride for many at 130 miles of mountain riding and Socorro, NM might be a good stopping point for you. For me, I must keep riding on my Trek Across America, as the days are moving ahead and the calendar does not rest for the wicked.