Achille Castiglioni (1918-2002), architect and furniture designer, left an enormous amount of inventions and designs, carefully kept by his family in his studio museum in Piazza Castello. Castiglioni's studio museum can be visited on appointment throughout the year.
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.
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.
Nice atmosfere, cool staff, opened from the first time in the morning til late night... Iter is a good choice for breakfast with coffee and brioche (the way Italians call the croissant), working days lunch (the have a fixed menu) and also for drinks - the menu changes seasonally and has always interesting options. Thanks to its location in a small street between the naviglio grande and pavese, the tourists somehow don't find it.