May, June, and September are the best months: warm, sunny, the sea swimmable, the crowds manageable. Easter (typically April) is a major celebration on Hydra and worth timing a trip around — the Good Friday epitaph processions through the streets, lit only by candles, are particularly atmospheric. July and August are very busy and very hot, and accommodation prices double.
The other event worth planning around is the Miaoulia, the annual festival in mid-to-late June commemorating the role Hydra's ships played in the Greek War of Independence. The week ends with a re-enactment of the burning of an Ottoman flagship in the harbour by fire-ship — a serious pyrotechnic display, set against the natural amphitheatre of the town.