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.

One of my favorite historical building from Milano, 

I consider e/c natural wine shop a hidden treasure in Milan. Inside a building with an "Emergency" (that is actually an ONG) plaque outside, the first thing one might think is that is a hospital. Once passing the wall, there's a cute internal square, with Basilica di Sant'Eustorgio view. You can sit both inside or outside, which a strongly recommend for spring and summer days. A nice place for just passing by to grab a bottle of wine and drink it at home, having a glass of wine (they have many options) or enjoying a relaxed evening.

Founded in 2011, Paladini 8 is a space of 500 mq which includes a backyard, a bar/bistrot, a vinyl and book shop, an exhibition room, a coworking space and a bunch of private offices with professionals in the creative field. Concerts, exhibitions and events are organised every night. This place represents an active and important landmark in the new cultural and artistic scene of Milan.

The owners were an industrial family of the XX century. We’ve been there a couple of times and we suggest it to every friend who is coming to town. You walk through the villa in the exact way they left it. You can see their personal pictures framed in the living room, their wardrobes and drawers full of stuff, like a pair of silk scarves especially designed by Monsieur Christian Dior for the sisters Gigina and Nedda Necchi, even the big marble’s bathrooms designed, like the entire house, by the architect Piero Portaluppi are inspiring.