Okay, so here comes an uncomfortable truth - The Haab is a good restaurant, but it's a bit boring. Before some frat bro goes in there and jumps on my spine (how dare you), let's have a dose of reality.
Alright, so when it came to my evaluation of Mexican joints, I have 4 categories. On the very bottom is Taco Bell, or any eatery that serve deep fried saddles of corn slathered with shredded lettuce, mechanically separated meat slime, shredded cheddar and "picante salsa" pretending to be Mexican It has as much right to call itself Mexican as Panda Express have to Chinese food - you might enjoy it for its craptitude or low cost, but never associate it back to the country that it was ganked from, because that shit is foreign to them. Next category is what I call Gringo - the stuff they serve to bros in the Cancun all-inclusives (hey, I am in Mexico and this is what they are serving me, so it must be for real, right?). Huevos Rancheros with coffee on the side, or some kind of aquas frescas that works well in cocktail mixers. Maybe an Enchilada slathered with sour cream (not crema) and half a jar of Goya mole sauce. Abuletas (Mexican grandmas) will slap the shit out of you for that, and most of your Mexican friends will nod politely while laughing about it with their fellow Mexican friends. On the Chinese food scale it's a bit like eating at Mission Chinese or Hot Joy - it might borrow the right ideas, and it might taste great, but don't you dare think of it as suggestive of the cuisine it's borrowing from.
The 3rd category is what I usually start with, and I'll call it the Barrio - the neighborhood joint in a Mexican neighborhood that is still rather gringo friendly - they have Tamarindos, flor de Jamaica and Horchatas in the Aquas frescas dispensers (usually off a syrup or a mix), and they got Postobon and Jarritos in the fridge. but they also got the real tacos (small tortilla, onions and cilantro, well flavored protein, choice of rojo or verde) and they know how to make a cemita or a torta sandwich. Solid good food, but it's not meant to challenge your boundaries. It's like ordering takeout from the local corner Chinese joint. It's hiding the regional variations from you, and you are not aware of how low a human will go to feed itself. It might be "authentic" in some sense, but it's a shallow knowledge.
The next and final category is what I nickname the "Santeria". Here you start seeing the full breadth and depth of Mexican cooking, with ingredients for tacos like Buche (stomach), Suadero (flank steak), Oraje (ears), Chupalines (grasshoppers), Chivo (goat), flor de calabaza (squash flowers) and Huitlacoche (corn smut), all of those are exceeding delicious when prepared with fresh ingredients. Your establishment will offer up raw radish slices (to munch on) and fried dried chiles (because you need that), and you can get a bowl of pozole (hominy and pork soup, Aztec style with Rosemary) there. It's like going to a Cantonese seafood restaurant or a Szechuan joint in Flushing. You get offal and weird seafood in the menu, and often strange preparations (like pickling crab in Shaoxing wine) that tests your culinary meddle - you want full culinary immersion? This is about as close as it can get without the need for a passport. Think of the 4 categories as like experiencing Mexican food in a Midwest shopping mall food court, the local Chipotle's, the local Mexican joint in Ridgewood/Greenpoint/Billyburg, and 5th Avenue in Sunset park.
So given those categories, The Haab is closer to the Barrio than the Gringo - foodstuff familiar to gringos, and maybe a few new discoveries, but nothing mindblowing. Sometimes you might see Tamales and Champurrados offered up, but that's just there to give the idea of "something different". Of course, the question is whether you see the neighborhood Mexicanos popping in - my guess is very likely no: No one with Mexican heritage nearby will spend $11 on Huevos Rancheros, especially when places on 82nd Street can do it cheaper. Plus they will usually just get a coffee with a bun at the local Panderia and work on weekends. Think of The Haab this way - it's an American brunch joint with Mexican influenced decor and some Mexican dishes (solid cooking, my wife's Enchilada Suiza and my Quesadillas both turned out well), but if you invite your local friends they'll tell you to hit a better spot that has more interesting things and a smaller pricetag (like the Colombian bakeries all over Sunnyside - El Pilon is a great place). That is not to say that the Haab is a bad restaurant - far from it. If I got company and just so happen to be in the neighborhood, I'll totally go there (as long as there is a free table). Just don't forget that there is an entire city out there with more interesting Mexican fare, and it's always a good idea to look further down the horizon.