New Mexico, sometimes abbreviated NM, (TV: The Zygon Invasion) was a state of the United States of America. In it could be found the town of Roswell, where the "Roswell crash" occurred. (PROSE: The Devil Goblins from Neptune, et al.)
The towns of Roswell, (TV: Dreamland) Truth or Consequences, (TV: The Zygon Invasion) Lamy, (PROSE: Atom Bomb Blues) Los Alamos (PROSE: Atom Bomb Blues) and Alamagordo (PROSE: First Frontier) were all located in New Mexico.
In 1945, the Seventh Doctor and Ace visited the town of Los Alamos. The town was closest to "the Hill", the American base for testing nuclear weapons during and after World War II. There, they opposed the machinations of Lady Silk. In order to get to Los Alamos, however, the Doctor and his companion first had to pass through the town of Lamy, where the duo were forced to leave the TARDIS. (PROSE: Atom Bomb Blues)
On a separate adventure in October 1957, the Seventh Doctor, Ace and Benny visited the White Sands Proving Grounds to view the launch of an Atlas missile. They also spent time canvassing the opinions of locals about strange goings-on at the Proving Grounds. Thus they spent some time in the town of Alamagordo as well. While there, Benny was offered the chance to go see Carlsbad Caverns, but she declined in favour of the chance to explore an Anasazi pueblo. (PROSE: First Frontier)
In the 2010s, the USA-Mexican border was among the places where newly-hatched Zygons were settled across the world as part of Operation Double, resulting in a minority of Zygons residing in New Mexico under the pretence of being British migrants. (TV: The Zygon Invasion)