To listen to Mexico's most traditional music, just head over to the mariachi plaza.
I visited Plaza Garibaldi for about a half-hour during a whirlwind tour with a cab driver of this massive city.
The young, the old, women and men _ all go there to listen to one-on-one private, yet public shows put on by bands who one can hire on the spot. Besides mariachis, there's also norteno bands one can hire.
Tequila, lots of tequila, is also sold at the plaza. People dance and sing next to the bands. I loved every minute of it. It was great to see all generations enjoy this timeless music.