Check out the local crags - beautiful hard sandstone around Droushia/Inia (20 min drive) and limestone in Diarizos valley (45 min drive).

You will find plenty of info on my friend's website (English translation coming soon!) or Cyprus Rocks.
Being a keen climber I will be more than happy to join you or find you a climbing buddy.
You will find a single rope and quickdraws at the Straw House so just bring your shoes and harness - nothing else!