The tourist season in Cyprus lasts from April to October. During this time there should be no trouble getting flights and hotels, all the attractions, restaurants and so on will be open, and there should be numerous activities and festivals to keep you occupied. The downside is, of course, overcrowding and inflated prices. Given a choice, try to avoid the fierce August heat (remember, Cyprus is just off the coast of the Middle East). If school holidays oblige you to visit the island in late July/August, make sure you’re in an air-conditioned hotel and are driving an air-conditioned car. The autumn, too, can be remarkably hot and humid, so don’t bank on cool, pleasant weather in September or even October. The best time to visit Cyprus has got to be the spring, when skies are blue, the air is warm and balmy, the uplands are a luxuriant green, the streams and reservoirs are full of water, and there are wild flowers everywhere. To further refine your choice, try if possible to be in Cyprus during the Greek Easter – it’s a major celebration in the Orthodox calendar, and there are interesting and picturesque events going on in towns and villages across the island. Much of this advice applies to the north as well as the south, though festivals will in general be Muslim rather than Christian, and the north coast can be cooler than the rest of the island thanks to mountain breezes from the Kyrenia Range.
During winter your experience of Cypriot life is likely to be far more authentic and less touristy, but a lot of places will be shut, and the weather will be more unsettled and even quite cold – a plus if you’re there to avail yourself of the island’s limited skiing opportunities, but a bit of a pain otherwise.