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.
Gramm Cafè is a super lovely place, born just few months ago in the warmest part of Milan: Navigli. Great for sharing some moments with friends, tasting great quality cocktails in a stylish designed interior. One of the best drink is for sure "Prete Rosso"!
An icon of 1930s art deco in the heart of Milan. Villa Necchi was built by Pietro Portaluppi for the Necchi Campiglio family, which belonged to the Lombard industrial bourgeoisie.
Loste Café is a Danish bakery opened by Stefano Ferraro and Lorenzo Cioli, two Italians who met at the star restaurant Noma, in Copenhagen. It's a simple (but with a good taste!) coffee shop, with amazing cinnamon rolls - Lorenzo is the former head of pastry in Noma - and a good option for a healthy quick lunch.
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.