Idraiki Gonia in the port of Hydra is a very good choice any time of day. You can come here to start your day on the island and enjoy coffee or one of the breakfast options.
You can either sit inside or outside, right next to the port. You can make a tasty stop here throughout the day and dine on Mediterranean cuisine of the seafood delicacies on the menu that tickle the taste buds.
You can make a date here for a relaxing drink in the evening.