Art and design museum in the Parco Sempione. Some permanent and some rotating exhibitions. Definitely visit the Casa Lana installation and the Italian Design permanent exhibit.

Rotating modern art exhibitions in a complex of. beautifully design/renovated buildings, designed by Rem Koolhaas. Also has a great cafe and restaurant.

Cozy ambient inside, but also with tables on the street, Champagne Socialist is a good place to try natural wines from Europe. You can also go there just to buy a bootle (or more, of course) and drink it at home.

Nilufar Depot: three storeys of historic and contemporary design, selected by Nina Yashar, one of Milan’s top design dealers. 

Absolutely delicious pastries and one of the best cappuccino in town.