Four Argentine presidents have been members of the stately Club del Progreso (dinner for two $45), in the Tribunales district. Since the restaurant’s revamp two years ago, politicos have returned for the modern takes on classic Porteño fare—mushroom-stuffed squid and tender suckling pig roasted in a clay oven—in the classic oak-paneled dining room. Highballs and Hurricanes are served with just the right degree of gravitas at the lacquered mahogany bar in Recoleta’s Hotel Club Francés (dinner for two $75). A recent makeover lightened the marble-clad interior with contemporary splashes of purple and ultramarine. In-the-know diners reserve a table at one of the city’s puertas cerradas, or closed-door restaurants, where chefs open their houses to a handful of patrons two or three nights a week. One of the movement’s founding institutions, Palermo-based Casa Coupage (dinner for two $190), is a wine lover’s dream: the sommelier-owners pair mineral-rich Chardonnays and dense Argentinean Malbecs with local dishes such as skirt steak with quinoa and portobello mushrooms. An unmarked doorway in Villa Crespo conceals Almacén Secreto (dinner for two $30), the private kingdom of chef Abigail Machicado, who prepares dishes from Argentina’s south (venison raviolones), center (oven-baked Paraná River fish), and north (charquisillo, a stew made with cured meat). In a country built on immigration, Koreans are among the latest wave of newcomers. At Cocina Sunae (dinner for two $50), Christina Sunae serves delicate pork dumplings and salads bursting with papaya and mango; save space for her green-tea ice cream.