Tenampa
Plaza Garibaldi 12
Plaza garibaldi, eje central in the corner of the garibaldi square, m-su 12pm-3am. the original and most famous mexican cantina, traditional home to the bohemians and mariachis of the 40s and 50s. huge selection of tequila and mezcal, light mexican food, and mariachi bands.
Centro Historico is the best place to partake in traditional cantina fare, including drinks where light meals and appetizers, called botanas, are served alongside for free. There are catinas everywhere in the neighborhood, all with interesting historical significance, live music, and interesting business types from the area. They are typically a male hangout, but women are accepted and safe, just be prepared to get some special attention if you show up.