Forgot about French Press. Not bad, but the acoustics are atrocious. You can't hear your own thoughts, it'll give you a headache before your food is served.
You want AUTHENTIC Mexican?? No ambiance whatsoever, but hit La Morenita grocery, where they serve traditional Mexican lunches. Also check out the shopping prices, they're straight out of the 1970's. Look at the spices while you're in there, you'll see a gazillion things you've never seen before (including spice bags containing wood chips... now what's THAT about? My wife lived in Spain for years, taught Spanish at UL, she didn't have any idea.)
Oh, and brush up your Spanish, because you'll be the only gringo in the place...