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.
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.
Craving proper Milanese food? Risoelatte is the answer to your prayers. Set in a cozy, 60's inspired location (complete with an original and working jukebox), Risoelatte is the perfect answer to the eternal 'what to do for Sunday lunch' questions.