Piazza dei Mercanti

A central and busy square in Milan, right near the Duomo. It boasts some grand and beautiful late-19th-century architecture. Once, and to some extent still today, it was an economic hub of the city, with the headquarters of several companies, and big banks and postal offices.

The grandest square in the city, the Piazza del Duomo is the cultural and social heart of Milan, and contains several of its most famous sights. There's the majestic cathedral and classy Galleria, plus the 18th C Palazzo Reale and several big, venerable buildings. The square is centred around the statue of King Victor Emmanuel II at Solferino – his horse is skidding to a halt as if it's just noticed the Austrian bayonets. The square is grandiloquent yet softened by its cafés, restaurants and shops, pigeons, and passers-by. Exchange kiosks here offer decent rates, better than those in the VE arcade.

Historical library that also houses the Ambrosian art gallery with treasures such as Leonardo Atlantic Codex.

The location of the Statue of Leonardo da Vinci and La Scala theatre. It is a small, but grand square flanked by fine palaces, such as the city hall and the commercial bank. Great place for a photograph and right next to Galleria Vittorio Emanuele. Ticket office is underground in the Duomo Metropolitana stop.

Massive, impressive and slightly mad: the cathedral is a late Gothic confection in white marble, festooned with spires and statues. You can admire the facade free from the piazza; getting inside or onto the roof involves three separate queues that may take over an hour, unless you book online. First locate the ticket office: it's along the street on the cathedral's south flank but has been known to wander, with various pop-up outlets. Here you queue #1 to pick up a number to queue #2 for the ticket desks. Buy your ticket, which will be for a specific time slot that day. When that time approaches (and off-peak it could be immediate) join queue #3 at the cathedral door for security and ticket check. There's a tedious list of what is and isn't allowed. Despite this list, shorts which end just above the knee are indeed allowed. Short-shorts are prohibited. Small backpacks are allowed (there is a bag check station). The interior is just as impressive as outside, though if you hate it you'll be in distinguished company. The problem was that construction went on in fits and starts for over 500 years, with every ruler adding bits or disliking previous work. Then in 1805 the conquering Napoleon said "Get this finished tout de suite, and my treasury will pick up the bill" and lo! it was finished. (Though he never paid up.) The Crypt of St Charles is entered within the cathedral, no extra fee, it closes around 17:00. The Baptistery of St John (extra fee) is within the cathedral. The roof (extra fee) can be reached by a lift or by 250 steps. The museum (included in ticket, closed W) is in the adjacent Church of St Gottard in Corte. It displays the story of the construction, with walk-in wooden models, façade designs from several centuries, sculptures and more.

A museum dedicated to one of the world's most famous opera houses. All types of memorabilias like dresses and pictures are on display. This includes a view into the opera hall from one of the loges, which is a short and simple alternative to the official guided tour of the opera. (Note that third party tour operators of the opera are not showing anything other than this view from the museum.) Check the museum website for the practice schedule, which determines visibility of the opera hall.