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.
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.