This is one of the shops that fits the bill. The characterful To Mavro Provato is located behind the dockyards, just before Koum Kapi. You can come here for an authentic time and enjoy tasty Cretan mezze, rakomelo and tsikoudias (raki).
The space is split over two levels and is characterised by its wood elements. You can try apaki, singlino with egg, sausage balls, kaltsouni with honey, fennel pie, potato stuffed with yoghurt and pork with graviera cheese here.