Aside from the obvious (sit on beaches, work on your sun tan, etc.) the following are all well catered for in Cyprus:

• Mountain biking - several companies can arrange the hire of bikes and provide trail information.
• Hiking - free trail information is available from the Cyprus Tourist Organisation.
• Water sports - wind surfing, sailing, kite surfing, etc.
• Hang gliding and para-gliding.
• Go skiing - Cyprus has a short but reliable skiing season on Mount Olympus. You can quite easily ski in the morning and sun-bathe on the beach in the afternoon.
• Diving - Cyprus has some quite good diving sites.
• Take in the extensive archaeological sights.
• Use Cyprus as a jumping off point for other major climbing regions. Easy access exists to climbing in Egypt, Jordan, and The Lebanon.