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Most places to eat at hotels offer a standard steak and seafood menu. Seafood, Mexican and Argentinian are some of the choices at eateries along the 3 blocks of Calle Basilio Badillo between Pino Suárez and Insurgentes.
If you want to sample authentic Mexican cooking and rub elbows with locals, try Cenaduria Doña Raquel, at Leona Vicario #131 (half a block east of the malecón). Along the back wall of a small, simple dining room, Mexican women whip up delicious flautas, enchiladas and tostadas in an open kitchen. The pozole (pork, cabbage and hominy stew) is excellent—and for the adventurous eater, also available with a “triple portion of head meat.”
For some of the city's tastiest and cheapest cuisine, grab a quick lunch at a sidewalk taco stand. You'll find them all over town, with an especially high concentration on the streets south of the Río Cuale in the Zona Romantica. Food vendor carts at the southern end of the malecón sell everything from fish on a stick to fresh-cut fruit. As is the usual case with street food and hygiene, use your best judgment. Does the operation look clean? Is it busy? If so, it's usually fine.
A casual dress code is the rule, although wearing shorts to dinner may be frowned upon at some of the nicer places. Some local restaurants shut down for a month during the summer.