What's the must-see thing in Milan?

The Duomo sits at the south end of Piazza del Duomo. Gian Galeazzo Visconti commissioned it in the late 14th century, and the last bronze door was set on 6 January 1965. You climb 250 steps to the rooftop (or pay €16 for the lift) onto terraces of pale marble, where spires rise close enough to run your fingers along the stonework. Even in late July, the stone feels cool underfoot while the piazza below pushes past 27°C and the air carries espresso and warm sugar from the gelaterie near the Galleria Vittorio Emanuele II. Go before 9am. By 10:30 the terrace queue wraps past the Museo del Novecento. Stair tickets cost €14 from the ticket office on the cathedral's south side.

Leonardo da Vinci's Last Supper fills the north wall of the refectory at Santa Maria delle Grazie, a 10-minute walk west of Cadorna station on Metro line M1. The church dates to 1401, the painting to 1498. You get 15 minutes in the room, and that is all anyone gets. Groups of 25 enter every quarter hour through a climate-controlled airlock that keeps humidity stable around the fresco. The painting is faded, flaking in places, roughly 4.6 by 8.8 metres on the wall. The composition still pulls your eye to Christ's hands the second you step inside, and the silence in that room is something you feel physically. Tickets cost €15 and sell out 2 to 3 months ahead through the official Cenacolo Vinciano site. No walk-ups, no exceptions worth counting on.

The Pinacoteca di Brera, founded in 1776 under Maria Theresa of Austria, holds what might be Italy's strongest single-room experience for painting. Room VI has Mantegna's Dead Christ from 1480, rendered in a forced perspective so steep that the feet seem to push past the canvas. Raphael's Marriage of the Virgin hangs two rooms over. Full admission is €15, and the first Sunday of each month is free. The Brera district around the museum tends to be the part of Milan that first-time visitors like best. The streets along Via Fiori Chiari stay shaded through midday, lined with small galleries and wine bars where an Aperol spritz runs €8 to €10. You'll hear live jazz from open doorways on Thursday and Friday evenings through September.

The Duomo and Brera are 15 minutes apart on foot through Via Manzoni. Do the rooftop first thing, walk north to the Pinacoteca by late morning, and eat lunch in the Brera quarter. Santa Maria delle Grazie sits about 20 minutes west on foot from Piazza del Duomo, so fit it around whatever ticket slot you managed to book. If your Last Supper slot falls in the afternoon, the walk from Brera passes Sforza Castle, founded in 1360, where Michelangelo's unfinished Rondanini Pietà sits in a ground-floor room that takes 20 minutes to see.