Both south and North Cyprus offer 300 days of sunshine a year, good food, friendly people and a wealth of ancient historical sites.
Personally, I recommend North Cyprus, because it�s much less developed than the south of the island. The countryside is breathtaking, the beaches vast and uncrowded, and the prices cheaper. The Turkish Cypriot food is great, the people friendly and eager to speak English, and flights get cheaper by the week.
You will love Kyrenia, a historic town with a stunningly beautiful harbour lined with great restaurants. Go in September and it'll be less crowded too! Try the Dome hotel for a taste of old-world comfort.
The best web site on North Cyprus by far is
http://www.cyprus44.com, packed with information and with links to cheap flights to North Cyprus.