The best months for Ithaca are May, June, and September. The sea is warm enough to swim, the hills are still green from the winter rains, and the island is quiet. Temperatures sit in the mid-twenties Celsius and the evenings are pleasant.
July and August are hot and busy by Ithacan standards — meaning the tavernas are full and the harbours have yachts at anchor, but you are not going to find anywhere genuinely crowded. The water peaks at around 26°C in August.
October still has warm days and quiet beaches; many tavernas close by early November, when the rains return. Winter is mild but wet, with most businesses shut and ferries less frequent. The Easter festivities (date varies) are worth catching if you are in Greece at the right time — the small island scale makes the candlelit procession on Holy Saturday especially memorable.