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.
A fairly new restaurant, managed by young people. The place is beautifully furnished, very minimal and reflects perfectly the quality of the food, a contemporary version of italian cuisine, but absolutely not artefact in its quality. Amazing ingredients, amazing food, and a special bravo to the sommelier.
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".