I found many links to newspapers from Latin America in http://www.plusnoticias.com/fdialatino.htm

The two listed under Argentina are the biggest here (La Nación and Clarín). I would include them in the right-ish political space. I would say that La Nación is the oldest and most traditional newspaper of the "elite", and cares a little more about the propper use of the language.

Try BBC Mundo. They have a whole section dedicated to Latin America. No adverts, free, and can get an app if you prefer it to the web version.

http://www.lanic.utexas.edu/la/region/news/mexico/

allyoucanread.com