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The triumphal arch of peace stands at the place at one of Milan's seven city gates. First the gate was known as Porta Giovia and was closer to the city center. Porta Sempione means "Gate towards Simplon", and once the road leading over the Simplon Pass to Paris went through this gate. The current gate was built in the early 19th century and at that time it was referred to as Arco della Pace.
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Branca tower
The tower is 108 m high built in 1933 and designed by architect Giò Ponti. From here you can get good views over Milan.
Parco Sempione
A big space of green land right behind the Sforzesco castle, and one of the most famous and popular in the city. Designed in like a neoclassical landscape garden, there are loads of features - such as a lake, the aforementioned arch of peace, a Roman-style sports' amphitheatre, a tower (which today hosts the Just Cavalli Hollywood), and several interesting features. It's a lovely leafy place to enjoy a walk at any time of the year. Reachable via Cairoli, Lanza, Cadorna or Moscova metro stations depending on what side of the park one refers to.
Sarpi
Not as big or famous as the ones in London or New York, Milan does also have a Chinatown, dating from the 1920s. Main street is the Via Paolo Sarpi, which is mainly a pedestrian street. Wide varieties of Chinese food is available. See Eat section for specific recommendations.
Santa Maria delle Grazie
Houses the famous Last Supper ('Cenacolo Vinciano') by Leonardo da Vinci. It is best to reserve tickets a few months before the visit. Canceled reservations are sold from 08:15 every morning (if there are any, best to show up in person). The church and the painting are inscribed on the UNESCO World Heritage List. If you arrive without tickets, you can buy a pass to five DaVinci museums for €38 that will get you in to see the Last Supper.
An elegant and aristocratic street in the north-western part of Milan. It contains sophisticated cafes and shops, and also some fine, mainly Baroque, palaces, notably the Palazzo Litta, one of the best examples of 18th century Milanese architecture, and also a place in which Napoleon I spent some time. Metro stations Conciliazione, Cadorna, Cairoli and Cordusio are the closest to the avenue. The famous Santa Maria delle Grazie church and convent, where Leonardo da Vinci's Last Supper can be found, is very close to the Corso.