What's a good 3-day itinerary for Milan?

Three geographic clusters, one per day, no backtracking. Day 1 stays within the rectangle between Piazza del Duomo and Via Manzoni. Get to the Duomo rooftop terraces by 8:30 AM, before the tour-group wave that hits around 10. The staircase ticket costs €10, the elevator €14. Up on the roof, the Gothic spires from the cathedral's 1386 founding stand close enough to touch, and on a clear morning you might catch a faint line of Alps to the north. Come back down and cross into Galleria Vittorio Emanuele II for a standing espresso at Camparino in Galleria, the old Campari bar pouring since 1915. By 11 AM, walk 8 minutes north to Museo Poldi Pezzoli on Via Manzoni, a private collection opened in 1881 where the rooms still feel like someone's home. Lunch at Luini on Via Santa Radegonda. The panzerotto fritto, fried dough stuffed with molten mozzarella and tomato, costs €3.50. Afternoon, the Teatro alla Scala museum on Largo Ghiringhelli lets you peer into the 1778 opera house from the box seats for €12.

Day 2 moves northwest to Santa Maria delle Grazie, the 1401 church on Corso Magenta. Book your Last Supper slot at least 2 months ahead through the official Cenacolo Vinciano site. The 15-minute viewing window starts and ends on time, groups of 25 at most. An 8:15 AM slot gives you the coolest light through the refectory windows, and the room smells like old stone, faintly damp. Leonardo finished the mural in 1498 on the refectory's north wall. Walk 10 minutes east to Sforza Castle, the 1360 fortress that now holds six museums under one €5 ticket. Michelangelo's Pietà Rondanini, his final unfinished sculpture, sits alone in a room at the back. Allow 90 minutes. Lunch at Latteria San Marco on Via San Marco 24 in Brera, a family kitchen with about 8 tables. The risotto alla milanese arrives deep yellow from the saffron, roughly €14. Afternoon at Pinacoteca di Brera, which opened in 1776 and still hangs Raphael's Marriage of the Virgin in Room XXIV.

Day 3 heads south. The Basilica of Sant'Ambrogio, dating to around 300 AD, is the oldest standing church in Milan, and the nave's stone acoustics carry every footstep. By 10:30 AM, walk 15 minutes south down Corso di Porta Ticinese to the San Lorenzo columns, 16 Roman pillars from the 3rd century. University students sit on the steps here most evenings with Peroni bottles, but in the morning you'll likely have the piazza to yourself. Lunch at El Brellin on Vicolo dei Lavandai, right on the Naviglio Grande canal. Order the cotoletta alla milanese, the breaded veal cutlet pounded thin and fried in butter until the crust crackles. A full plate runs about €18. The Navigli canalside tends to feel quiet before 5 PM, which is when the aperitivo bars start setting out buffet spreads. A Negroni Sbagliato, the sparkling-wine variation that Bar Basso on Via Plinio claims to have created in 1972, costs €8-10 at most Navigli spots.

Milan's Metro connects all three days' starting points. A single ride costs €2.20, but a 48-hour pass at €8.25 pays for itself by the third trip. To be fair, Milan is not cheap for eating out. A sit-down lunch with water and a primo runs €15-20 per person in most neighborhoods. The standing-bar espresso culture saves real money, though. At current rates, 1 USD buys about €0.88. Worth noting, the afternoon heat in late July currently reaches about 27°C, warm enough that an indoor museum break between 2 and 4 PM feels less like scheduling and more like survival. The three days cover roughly 28 kilometres total, about 7 on foot each day, the rest by Metro and tram.