There are only a few authentic Mexican restaurants.
If you like it hot, you should order it extra spicy anywhere you go in Moscow because Russians don’t really have a taste for spicy food.
La Cantina on Tverskaya is a rowdy restaurant where the live music is loud, even if the cover bands are questionable, and the tequila is always flowing. It’s a popular expat place. My Mexican friends like the food at Casa Agave in Kitay Gorod and Amigo Miguel at metro Aeroport just outside the city center.