Flowers lovers! Orto Botanico di Brera is an hidden treasure right in the center of Brera and near by Pinacoteca.
The garden is a university and museum, there they organize events and activities for the public and schools. It has an amazing collection of flowers and medicinal plants, plus little corners where you can stop by and enjoy the silence for a bit.
Giacomo ristorante, bistrot... They are all located on the same street, Via Pasquale Sottocorno, but the rosticceria is the more, let's say, "easy-going" (and the cheapest) of the three.
It's a good place for lunch and dinner - ask for a table at the "giardino interno".
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.
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.