The Jesuit Block — Córdoba's historic heart, and its UNESCO treasure, is the Manzana Jesuítica — a colonial block built by the Jesuits, holding their Baroque church (with its remarkable carved cedar ceiling), their college (the Colegio Nacional de Monserrat), and the University of Córdoba, founded in 1613 and the oldest in Argentina, with its old cloisters and library. Touring the church, the cloisters and the university, you trace the Jesuits' extraordinary educational and missionary project in colonial South America — the reason this learned city is nicknamed "La Docta." It's the essential historical experience.
The colonial centre — Around the Jesuit Block, Córdoba's colonial centre rewards a wander — the Plaza San Martín with the cathedral (a fine, eclectic colonial-and-later church) and the whitewashed Cabildo (the colonial town hall, with a dark museum of the last dictatorship in its cells), the pedestrian shopping streets, and more colonial churches. It's a real, working Argentine city centre rather than a tourist showpiece, busy and everyday, with the history woven through. Combine it with the Jesuit Block for the full colonial Córdoba.
Student energy, nightlife and cuarteto — Córdoba is one of the great university cities of Latin America, with a huge student population, and that gives it a famous, youthful energy — a nightlife that runs very late, a strong bar, brewery and café scene (especially in Güemes and Nueva Córdoba), and its own music: cuarteto, an infectious, danceable local genre (Córdoba's own), played in packed dance halls. The bohemian Güemes barrio, with its Saturday craft market and design shops, is the creative heart. Go out late, dance a cuarteto, and drink the local ritual — fernet with cola, which Córdoba consumes with a passion.
Argentine food and the Sierras — Córdoba eats Argentine, which means beef — the asado (barbecue), and the local empanadas cordobesas (slightly sweet, with a sugar dusting), locro (a hearty stew), and, of course, Malbec and Argentine wine, with medialunas and alfajores for the sweet. And the city is the gateway to the green Sierras de Córdoba — mountains, rivers and reservoirs, hill towns like the German-flavoured Villa General Belgrano and La Cumbrecita, and the Jesuit estancias (Alta Gracia, with its estancia and Che Guevara's boyhood home; Jesús María; Santa Catalina) in the countryside. Eat an asado, drink a fernet, and get out to the Sierras.