Take a hike
The focal point of Milan is the Duomo, one of the largest cathedrals in the world. From the Duomo, walk through the elegant Galleria Vittorio Emanuele II.
You emerge in the Piazza Scala, with the Teatro alla Scala – one of the world's premier opera houses – looking surprisingly modest. Walk down the street to the right of the Scala, the Via Verdi, which is lined with boutiques and galleries. It continues north as Via Brera.
Lunch on the run
You hear Bar Brera at Via Brera before you see it — the terrace outside is always lively. Pastries, sandwiches and all kinds of Mediterranean delights are on offer for lunch from Tuesdays to Saturdays.
The marvellous Pinacoteca di Brera, part of the palace at Via Brera (8.30am-7.15pm daily except Mon), is a showcase for masterpieces by some of the great artists of the 13th to the 20th centuries. Highlights are Mantegna's Lamentation of Christ and Raphael's The Marriage of the Virgin altarpiece. Caravaggio, Piero della Francesca, Rembrandt and Goya are also represented.
Lavori in corso, "work in progress", evident everywhere in Milan, is especially irksome on one of the primary shopping streets, Via Montenapoleone, or "Montenapo". Showcases for luxury brands such as Versace, Prada and the flagship Gucci store are half-hidden while the road is dug up. The parallel Via della Spiga offers Miu Miu, Roberto Cavalli and Dolce & Gabbana.
To spend rather than merely window-shop, one of the more personal and unusual stores is south of the Duomo: for a hand-made handbag, visit Travi at Corso di Porta Ticinese (9.30am-7.30pm daily except Sundays).
Dining with the locals
At the top of Corso di Porta Ticinese, you can see 16 Corinthian columns from a pagan temple of the 2nd to 3rd century AD – and, behind them, the San Lorenzo alle Colonne, a superb 4th-century basilica.
You can also see ZeroDue at number 6. This stylish restaurant (open daily except Monday) is named after the dialling code for Milan, 02.
It occupies part of the remains of a 15th-century convent on Roman foundations. Beneath the brick arches, dine on penne alla puttanesca (with tomatoes, capers and olives), or the house salad, which is laden with chicken and blackberries.
Go to church
The artistic pinnacle of Milan — and arguably Italy — is Leonardo da Vinci's fresco of The Last Supper, painted on the wall of the refectory of the convent of Santa Maria delle Grazie, in the west of the city.
Book online at www.cenacolovinciano.net for a 15-minute slot as soon as you buy your tickets — don't wait until you arrive in Milan. Tickets are available 8am-7.15pm daily except Mondays and May Day.
A walk in the park
The 15th-century Duke of Milan, Francesco Sforza, was the man responsible for both Santa Maria delle Grazie and the reconstruction of the fortress known as Castello Sforzesco (7am-6pm daily) at Piazza Castello. The castle houses a collection of museums, but on a fine day your attention will be drawn to the vast, elaborate Parco Sempione – the largest green space in central Milan.
Out to brunch
Feast your way through the Mediterranean buffet, served on Sundays from noon to 4pm, at the Cantina della Vetra at Via Pio IV. This big, busy and very popular enoteca serves an array of charcuterie, seafood, vegetables and sticky desserts in abundant quantities; the price includes coffee.
Take a ride
Milan has recently acquired a bike-rental scheme, named bikeMi, with stables of bicycles dotted around the city – including one outside the Cantina della Vetra. Register for the day, but as long as you keep each individual hire to less than half an hour there's no further charge to your credit card — you can use a bike as often as you like.
The trams in Milan take you back to a different era — many of the 1920s editions are still running.
Buy a ticket from a tobacconist or metro station, then hop aboard tram 2 or 14 going north from Largo Carrobbio, making sure to stamp the ticket at the machine at the front. It zig-zags north, and you should get off where the lines cross Via Paolo Sarpi. Then walk a short way east to the final stop.
The icing on the cake
The collector and entrepreneur Carla Sozzani has created a concept store in a former Fiat garage at 10 Corso Como, whose name is also the same.
In a shady courtyard full of greenery, art, home furnishings, books, music and clothes are sold under one roof, alongside a restaurant (half of which spills out into the courtyard) which serves modern Italian fusion food. There is an excellent (and free) gallery.