My family always think of The Lady with an Ermine as 'our' Leonardo because it comes from the Czartoryski Museum in Kraków, my father's home city. Yet the painting's temporary absence abroad – as star of the National Gallery exhibition – has not drastically diminished the attractions of the old Polish capital. I have been visiting Kraków since I was a child and its style and atmosphere remain for me unique.
All round the clock, life centres on Rynek Główny which, though majestic in scale as one of the largest market squares in Europe, is no bleak formal space. Surrounded by mansions with substantial stone portals and bisected by the ebulliently crenellated cloth hall, Sukiennice, it celebrates a city delighted to be part of Renaissance Europe. Locals make brisk diagonals from point to point while visitors take a passeggiata round the edges. Inside Sukiennice, traders sell the traditional Polish souvenirs of carved wooden chess-sets, dolls in folk costume, embroidered linens and amber. Beneath it, a new museum reveals the excavated foundations of mediaeval market stalls and burial sites, finds lost by careless burghers – hairpins, gaming counters, coins – as well as presenting films and virtual reconstructions of the city's history from its origins at the crossroads of key trade routes from the Baltic to the Black Sea.
The Mariacki church presides over Rynek, set assertively at an angle with two unequal towers supposedly built by two brothers, one of whom killed the other to ensure his tower was the taller. Not only is it encircled by a gold bauble-tipped corona, but from here on the hour, every hour, the plaintive hejnał bugle call sounds across the city, terminating abruptly at the point when, in 1241, the lookout was shot by a Tatar arrow. The church's greatest treasure is a magnificent altarpiece commissioned from Veit Stoss (Wit Stwosz) in 1477, which took the Nuremberg master sculptor 12 years to complete.
Kraków is an easy city to explore on foot, Rynek providing orientation at the end of pedestrianised streets radiating out on all four sides. There are also traditional droshkies. When we first clambered aboard, my father remarked that the driver seemed drunk. "Don't worry," reassured his cousin, "the horses know the way." On the south side, Grodzka Street leads to the royal palace of Wawel and its cathedral, its massive brick ramparts topped by a fabulous cluster of towers and turrets. This is how castles ought to be, the triple tier of arcading round the central courtyard perfect for viewing tournaments. Within are the royal treasury, state apartments with deep coffered ceilings and walls covered in Flemish tapestries, as well as oriental carpets, banners, sabres and saddles, captured in 1683 by King Jan Sobieski from the Turks at the gates of Vienna.
West of Rynek, the Oxbridge-like Collegium Maius lies at the heart of the Jagiellonian University, founded in 1364. Its museum contains scientific instruments used by Copernicus in the 1490s, confirming Kraków's part in the international culture of humanism. Poland's most famous 19th-century painter, Jan Matejko, was born and died in a house on Florianska Street, north of Rynek. The house of his pupil, Stanislas Wyspianski, on Plac Szczepanski, is also open to visitors, creating with the Conservatory of Music and Palace of Fine Arts, a corner of Jugendstil architecture. Both artists were committed to the conservation of the city, a cause identified with Polish nationalism under 19th-century Austrian rule.
Sometimes considered a mini-Vienna, Kraków, too, is ringed by gardens where the city walls once stood. Ten minutes' walk south, in the old Jewish quarter of Kazimierz, the depredations of more than half a century are being reversed through the restoration of synagogues and growth
of a vibrant social life with restaurants, bars and bookshops.
Across the river Vistula in Podgórze, is Oskar Schindler's enamel factory, now a branch of Kraków's historical museum, which documents the experience of living in the city under five years of German terror. Through the decades of communism, the city stagnated, though it thereby evaded the worst excesses of post-war planning. There has been much modernisation during the last 20 years, including the opening in 2011 of that global sine qua non of urban regeneration, a contemporary art museum, MOCAK. Its impressive first show was devoted to history in art, appropriate for a city so richly endowed with both.
Celina Fox is author of The Arts of Industry in the Age of Enlightenment (Yale).