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.
To really reach/understand a city you must live there or, at least, acting like you do. Nothing makes you feel more like a Milanese D.O.C. than stopping by Frida's on a Sunday morning to buy some flowers. Located in Brera this tiny shop has an extraordinary colour palette of flowers and plants. After that we just take a walk in the neighbourhood holding our bunch of Brassica Oleracea and our day is made.