Samos is the birthplace of mathematician Pythagoras, so if you're old enough to have put the trauma of those maths classes behind you, wandering around this pretty World Heritage-listed town is well worth it. Highlights include the ruins of Aphrodite and the Eupalinos Tunnel built in 524BC.
Lesbos is famed for its scenic hiking trails which meander around mountain paths in the north and south of the island - Vatera-Yera and Petra-Lapsarna are two popular ones. The hot thermal springs at Therma Yera are perfect to ease any aches and pains afterwards.
On Thassos, visit the old Roman market place, temple of Athena and acropolis at Agora, or just wander around the ancient Thassos Town.
If go on holiday to the Aegean Islands during the summer months, you can take a ferry from Samos to the popular Turkish resort of Kusadasi just three kilometres away. Kusadasi is close to the ancient Roman town of Ephesus with its superbly intact amphitheatre and other buildings.
From Chios you can also visit Turkey, Cesme is just across the eight-kilometre wide Chios Straits.