The University Libraries home page - database section - offers several sources for newspaper articles online, both historical and contemporary. To use them you need a UNM login or to be working at a UNM Library computer.
The databases are grouped under Alpha letters.
Under Alpha N - Newspapers - Newspaperarchive - Accessnewspaperarchiveonline - you can limit for New Mexico newspapers - has scanned news pages for Santa Fe from 1849-2015 and Albuquerque and Las Vegas from 1880-1977. There are some newspapers from more recent decades for other New Mexico communities. (Access Newspaper Archive Online can also search newspapers in other states and some countries).
Alpha C - Chronicling America (Library of Congress website) - has scans of New Mexico Spanish language newspapers before 1922. (It also can search early newspapers in other states).
Alpha N - New Mexico Newspapers - has online news articles for Albuquerque since 1995 and Las Cruces and Roswell since 2004.
Tip: Also see another useful related libguide about newspapers for this area and beyond.