Milan

The roof is open to walk on, so the marble carving stands right at your face between the spires. Stairs cost less and the queue forms at the lift. The marble came by boat from a quarry up by Lake Maggiore, and repairs still take stone from there.

A cross-shaped arcade under a glass roof, joining the cathedral square to the Scala. Turning three times on your heel on the bull in the floor mosaic is meant to bring luck, so that one tile wears into a hole and is replaced every few years.

Numbers and time are both fixed, so the visit is over in fifteen minutes. Tickets are released months ahead and mostly go then, which leaves next to nothing for anyone deciding late. It was painted on a refectory wall, and the paint began falling early.

The season opens on 7 December, Saint Ambrose's day, and the whole city talks about it. Cheap standing places in the gods go on sale that day at a side window, with half the stage in view. A museum ticket looks into the auditorium when nothing is on.

The courtyards can be crossed without a ticket, and people cut through as a short way somewhere. The Rondanini Pieta, which Michelangelo worked on days before he died, stands apart in an old hospital hall, unfinished, the two bodies still joined.

The art school is in the same building, so students pass on the stairs carrying their gear. Mantegna's dead Christ, seen from the soles of the feet upward, hangs here, and that one room takes the crowd. The garden in the courtyard needs its own booking.

The cathedral's marble came in along this canal, and Leonardo had a hand in the lock design. Both banks are bars now. They fill once the sun is down. An antiques market runs along the water on the month's last Sunday.

Ambrose, who watches over Milan, founded this church, and his remains lie under glass in the crypt. A cloister closes the forecourt on all four sides, and the traffic noise stops at the gate. Brick is the whole of it, with no marble anywhere.

Two residential towers with grown trees on every balcony, whose summer leaves shade the flats and cut the cooling load. Gardeners work the face on ropes to keep them, and once winter strips the leaves it looks like another building. Nobody goes inside.

Families commissioned sculptors for their plots, so each tomb is a small piece of architecture. One has the entire Last Supper cast in bronze, and fashions from the century's first decades are set here as they stood. A map is handed out free at the gate.

Plain stone outside, but inside, the walls and vault are covered end to end in sixteenth-century fresco, so Milan calls it its Sistine Chapel. A central wall splits the public church from the nuns' hall, which you reach by a side door. Entry costs nothing.

Library and gallery founded by Cardinal Borromeo in 1609. Caravaggio's Basket of Fruit hangs here, as does Raphael's full-size cartoon for the School of Athens. Pages of Leonardo's Codex Atlanticus go on show in rotation.

Twentieth-century Italian art in the Arengario beside Piazza del Duomo. A spiral ramp climbs to Lucio Fontana's neon-ceiling room, whose big window looks straight at the cathedral front. The huge painting at the entrance is The Fourth Estate.

A street behind left no room for a deep choir, so Bramante painted one in perspective. From the front a coffered vault seems to run far back; a few steps to the side and it flattens into about 1 metre of depth. Duomo visitors can reach it in minutes.

A contemporary art centre in a former distillery on Milan's southern edge, reworked by Rem Koolhaas and opened in 2015. The Haunted House, sheathed in gold leaf, is the building you notice. Bar Luce inside was designed by the film director Wes Anderson.

The old upper town of Bergamo, sitting on its hill a train hour from Milano Centrale. A funicular climbs from the lower city, and walls built by the Venetian Republic ring the hill. UNESCO has listed those walls since 2017.

A side chapel in a small church east of the Duomo, its walls patterned with human bones and skulls. Tradition traces them to an old hospital burial ground. No admission charge, and it takes only minutes.

A 1930s house of wealthy Milanese, now run by the heritage trust FAI. Visit on your own with an audio guide (Korean included) or join a guided tour. The garden pool was the first built on private land in Milan, and the film I Am Love was shot here.

The block framed by Via Montenapoleone, Via della Spiga, Via Manzoni and Via Sant'Andrea gathers the luxury flagships. Milanese call it the fashion quadrilateral. The seasonal sales begin at the start of January and of July.