El Mariachi caters to Mexicans (most of the signage is in Spanish, as are the printed receipts) and accordingly has no labeled vegetarian food on the menu. You can have them construct a taco or tostada but it won't be anything you couldn't have done at home with lettuce, tomatoes and a tortilla. Avoid the beans and rice, as the former is cooked with lard and the latter with chicken broth.
Given their location on Nicollet, I'm surprised they don't even attempt to attract a more diverse crowd with vegetarian options or even a token "vegetarian" section on the menu with cheese enchiladas and avocado.
While they do serve free chips and salsa, I found the chips to be overly salty and the salsa was more like a thick marinara sauce, rather than a fresh and light pico de gallo with tomatoes, onions and herbs.
Come here for the bar and the music (which can get pretty loud, by the way). Their mixed drinks are tasty but quite expensive at $7-9 a piece. Better stick with a Corona next time.