Gold and silver mining were major occupations and attractions in that period, especially around Silver City, Grant County, NM. The boom included Pinos Altos, Hanover, Georgetown and dozens more. Lots of the activity continued into the teens and twentys.
The state of New Mexico was established from the Territory in 1912, so 1900 archives might be a good place to start narrowing down your search. Some of the towns are no longer populated, such as Lake Valley. Some are semi-touristy places, but with a solid foundation in mining, such as Magdalena, Winston, Mogollon, Kingston and White Oaks. I have probably forgotten some important ones, but check with the NM State History site. Remember to note how HUGE the counties in NM were, and when they were divided.