This aesthetic treasure-trove, amassed by the incredibly wealthy Giacomo Poldi-Pezzoli in 1881, is filled with collections of jewellery, porcelain, sundials, tapestries, ancient armaments, period furniture and paintings. Botticelli's masterpiece, Madonna and Child, is alone worth the visit.

Pollaiuolo's girl in pearl earrings rivals Vermeer's, easily holding her own among angelic-action-packed Tiepolos and Moroni's smirking knight in black. One room showcases timepieces, including one boastful watch painted with women admiring it; another chamber features chests engraved with maps showing Australia as a porcupine.

Milan's Duomo is the world's fourth-largest church. This late-Gothic wonder features a forest of spires and statuary, marble pinnacles and pillars, all woven together with a web of flying buttresses. Gian Galeazzo Visconti had grand designs on the city in 1387, and rallied support for the massive new Duomo. The view from the roof is the city's finest.

To win over naysayers, Visconti agreed to cover the cost of the lavish pinkish-grey Candoglia marble. Yet, as the edifice went up, engineers denounced the massive structure as unscientific and unconstructable. The marble was nice, but how could the largest slabs be transported through the narrow streets to the centre?

As always in Milan, there was also the matter of style. By the time the cathedral began taking shape, the rest of Italy had moved on from French-inspired Gothic. But rather than stripping away Gothic ornament, Milan piled it on, literally taking Gothic to the next level with spires capped by thousands of sculptures in a fusion International High Gothic style.

Don't be surprised if some of its splendours are under wraps when you visit - like certain ladies who lunch in the Quadrilatero d'Oro, the Duomo gets a little work done to its face and backside on a regular basis.

Take a long, hard squint because, despite restoration efforts, this masterpiece is gradually fading. In 1495, Leonardo da Vinci was commissioned by Ludovico Sforza to paint the wall of this convent. He painted the iconic Last Supper in an experimental mix of tempera and oil which, whilst brilliant then, has been peeling off the walls ever since.

To visit the refectory of the Convento di Santa Maria delle Grazie you'll need to plan ahead. There are tales of travellers who managed to get in without making prior arrangements, or get in as part of a one-day Milan tour, but such miracles seem reserved for the truly faithful.

Founded in the 4th century by Milan's patron saint Ambroggio, this church has been repaired, rebuilt and restored many times and is a hotchpotch of styles. The shorter of the two bell towers dates to the 9th century as does the canopy over the altar inside. The saint himself is buried in the crypt and his body can be viewed in spooky desiccated form.

Ambroggio rose to power rather suddenly, graduating from public servant to bishop in about a week after rowdy Milanese crowds demanded his appointment. Sant'Ambroggio proved to be a quick study and unusually gutsy, a staunch defender of the poor and opponent of Arianism, Lombardy's main religion at the time. For all his successful politicking, he wouldn't sacrifice principle for diplomacy - he demanded that Emperor Theodosius repent for the massacre of 7,000 people at Thessolonica under threat of excommunication.

The church itself is a fitting legacy: the solid brick structure is well grounded, and its purposeful simplicity is truly uplifting. Once inside, your eye may be caught by the shimmering altar mosaics and AD 835 gilt altarpiece telling Sant'Abroggio's life story - but wait until you see the 4th-6th century mosaics inside the Sacello San Vittore in Ciel d'Oro.

'Untutored hands may not touch me', are the words of a true diva, inscribed here on an 18th-century spinette (piano). Harlequino costumes and playing cards left at La Scala also hint at centuries of Milanese musical drama. Portraits show Rossini chatting up patrons, while Verdi seems troubled by mixed reviews, and Callas a goddess towering above critique.

There's nothing exceptional about this Milan institution when compared to the many funky new bars around, but its location on the cobblestones in the heart of historic Brera make it perennially popular with locals and tourists alike, especially on a sunny afternoon.

Belle and Sebastian, Artic Monkeys, the Yeah Yeah Yeahs and local bands you never heard of (but should) play Milan's leading rock venue. Patrons have been known to shower bands with adoration and contempt by spraying them with beer from the bar above the stage, but nowadays management keeps a look out for amp-destroying rabble-rousers (you know who you are).

When an entire former warehouse full of people is working up a sweat to indie international acts, cutting-edge DJs and the best local bands, there's no cooler place to be in Milan. Can't argue with the price either. Wednesdays are Night of Contemporary Beat, and the legendary Jet Lag Fridays are free with a drink.

Like a little black dress, Il Coriandolo is the classic choice to accompany gallery openings or business meetings. The house spumante is a worthy prelude to house-made truffle ravioli with butter and crispy sage, whether you've come for a power lunch in a leather banquette or scintillating dinner conversation in the covered garden.

Founded in 1817 by a soldier in Napoleon's army, this elegant tearoom has languished on Monte Napoleone since 1950 (the original was destroyed during WWII). A popular shopping stop, you can either shoot an espresso at the bar or relax over drinks in one of the sitting rooms.

If you've witnessed the sights and smells of Peck and want to experience their food (minus the formal setting of Cracco-Peck), this is the place. A regular lunchtime crowd fills this modern eatery by 1pm, but they serve a full menu through to 8pm, so it's good for a late, late lunch. The quality is excellent, the servings generous and there's a good wine list.