Colonia Centro

Establishment neighborhood
Churros El Moro
Eje Central Lázaro Cardenas 42, Colonia Centro
This legendary "churreria" has been open in the same locale in the Centro since 1935 when the Spanish owners bought the property and imported the Spanish fried-dough delicacy to Mexico. They've been going ever since, in the same old building, with floor to ceiling tiled interiors, and the same menu of churros and four hot chocolate varieties—the thick Spanish version, traditional French style, cinnamon and vanilla-infused Mexican variety, and Swiss, which comes with whipped cream. There are a couple of new specialties on offer, including their take on the ice-cream sandwich, but nothing beats dipping a plain churro into a mug of hot chocolate. If the Centro is too much of a journey, they have a new stand at the Mercado Roma.
Culinary Backstreets Walking Tour
So this isn't a specialty shop at all: it's actually a website and awesome tour company that organizes several monthly food tours in the Centro Histórico (and will lead you to some of the best specialty shops and purveyors). They've done an amazing job of finding rad street food stands and old-school treasures, and creating a totally enlightening tour that doesn't feel trite or touristy in the least. It's worth booking ahead as their small expeditions fill up quickly.
Dulcería de Celaya
5 de Mayo #39, Colonia Centro
This is one of the most beautiful candy shops in Mexico, if not the world. In the same spot in the Centro for over a century, the space itself is a relic from a time past: The wooden display cabinets, baroque-style mirrors, and even the sign haven't changed in over 100 years. The sweets haven't changed much either, as the Dulceria is one of the only places where you can still find such an array of traditional sweets from cajeta, to mazapan, to cocadas, to an insanely sweet, perfectly moist pay de rompope (eggnog cake).
El Danubio
Republica de Uruguay 3, Colonia Centro
In the same location since 1936, this Basque seafood restaurant is an old-school classic with the requisite white tablecloths and dressed up waitstaff. Located in the Centro, it's where businessmen and politicians entertain, eating traditional paella, Lobster Thermidor, fresh langoustines, and big seafood platters. With 110 dishes on the menu, it's hard to believe that everything is fresh but there's a reason this place is legendary—all the fish and shellfish are flown in each day, and every single dish on the menu is made to order.
Azul Histórico
Isabel la Cátolica 30, Colonia Centro
Ricardo Muñoz Zurita, the chef behind this small chain of restaurants, has developed and re-discovered certain moles and salsas that were otherwise almost totally unknown in Mexico City, even among serious foodies. The Mole Negro, heavily condimented Chipotle salsa, and Oaxacan tortilla soup are just a few of the highlights that also happen to be among the most affordable when it comes to serious gourmet eats in town. Of his four restaurants, his latest opening on the patio of a 17th-century palace, is definitely the most glamorous, and a heavenly break from the Centro's busy streets.
El Cardenal
Calle de la Palma 23, Colonia Centro
Don't let its location in the Centro's Hilton fool you into thinking this is a tourist trap: El Cardenal has been around in several incarnations since the 80's and is one of the more formal restaurants for Mexican food, where high-fliers take their business clients and families do Sunday lunch. The menu is extensive and for newcomers, a perfect introduction to regional cuisine, from their traditional Chiles en Nogada to Enchiladas, to whole roasted fish and tacos de Arrachera (steak)—the best in town. Beyond lunch, though, breakfast is where it's at with a selection of freshly baked pastries, authentic hot chocolate, freshly squeezed juices, and traditional egg dishes—the ultimate mix of sweet and savory.
Mercado de la Ciudadela
Mercado de la Ciudadela, Av. Balderas, Colonia Centro
If you're in the market for crafts and mementos, this covered artisans market is kind of a must. You'll sift through a lot, and will need your best negotiating skills, but it's a great stop for papier maché figurines, paper flowers, hand-blown glassware, traditional kids toys, and plenty of papel picado—all great for gifts to take back home as well as party decór. If you come on a weekend, don't miss the public salsa, merengue, and danzón dance party attended by elderly couples on the square just across the street.