The first stop for most tourists is to pay their respects to the breathtaking Duomo (piazza del Duomo, 02 8646 3456). Some 3,500 statues adorn the exterior of this vast cathedral – the third largest in Christendom – which was started in 1386 and finished in 1805 because Napoleon wanted to be crowned King of Italy there. If you are lucky enough to visit on a clear day, the view from the roof reaches as far as the Alps, over 60 miles away. From the Duomo, it’s a short walk to La Scala, via the exquisite Galleria Vittorio Emanuele II. Completed in 1867, this glass-roofed arcade with marble flooring was built to accommodate shopping, strolling, people-watching and coffee-drinking. The opera itself is only in season from 7 December to the end of June; try for tickets on 02 7200 3744, www.teatroallascala.org. But you can always visit the theatre’s museum.

North of the Duomo in Brera is the Pinacoteca Brera (via Brera 28, 02 722 631, closed Mon), Milan’s best art collection, covering 700 years of Italian art. Treasures include Raphael’s Marriage of the Virgin, Piero della Francesca’s Brera Altarpiece, and works by Titian, Canaletto and Caravaggio.

Further art is on view at the Castello Sforzesco (piazza Castello, 02 884 63700, closed Mon), including the Rondanini Pietà by Michelangelo, and works by Mantegna, Bellotto and Canaletto.

Behind the Castello is the Parco Sempione, one of the few green areas in central Milan. The Triennale building (viale Alemagna 9, 02 724341, closed Mon) is an obvious mecca for all design fans. Apart from the exhibitions, the café is a big draw: the chairs are all copies of famous modern designs.

The defining intellectual and moral figure in Milanese history is Saint Ambrose, bishop from 374 to 397AD. At the time, Milan was the capital of the western Roman Empire, although the current Lombard Romanesque design of the Sant’Ambrogio church complex (piazza Sant’Ambrogio 15, 02 8645 0895) dates from the 11th century.

Another famous adopted son was Leonardo da Vinci. He spent 24 years away from Vinci working for the ruling Sforza family. You’ll need to book four weeks in advance (02 8942 1146) if you want to see his Last Supper (Santa Maria della Grazie, Piazza Santa Maria delle Grazie 2, closed Mon).

Leonardo, being the supreme multi-tasker that he was, also helped design the locks and canals (navigli) that served as Milan’s commercial lifeline. Only the Naviglio Grande and Naviglio Pavese remain. The Navigli district, where they converge, is now a focus for trendy boutiques, bars and restaurants.

• Tourist information: via Marconi 1 (02 7252 4301, www.milanoinfotourist.com).