I go to Chios almost every summer. Once there, the island traps you and you want to come back over and over... It is not easy to forget the wild landscape, the beautiful beaches, the waterport in the town with the small lights at night and of course the great food...
Chios is not famed for the beaches, although Trahili and Mavra Volia are among the best in Greece. It is famous for the villages with the strange architecture, the small forests in between, the mastic trees in the south, the good-hearted people. Have a coffee in a Greek coffee shop in a village square under the plane tree, taste mastic sweet, buy cosmetics of mastic, take pictures of the mountains, see the Castle and the cave in Olympi, taste cheese pies.
Last summer, we took the boat to Oinousses. This is a small island about an hour from Chios. It is a unique opportunity to see an isolate Greek island, although in summer it gets a bit frequented. If you have a passport, also take the boat to the opposite coast of Turkey and visit the historical town of Cesme and Izmir. Tour boats leave in the morning and return in the evening.