Ios has some very distinctive and unique traditional products. You should definitely try the local cheeses: white kefalotiri, xyno (sour: soft white cheese), skotiri (mix of cheeses and aromatic herbs) and sweet myzithra.
You should also try the local pastries, such as pasteli, xerotigano (diples), amygdalota (marzipans) and pure thyme honey.
All the restaurants and the taverns serve amazing delicacies, like revithokeftedes (from chickpea), tomatokeftedes (from tomato) and tsimetia (stuffed zucchini blossoms).