I had a brilliant 100+ miler when I was there a few Christmases ago, also staying in Paphos. Out along the coast road about 10-15 miles, then inland through the mountains and to the top of Olympus and back. A long serious solo ride, but one of my top outings of the last 10 years.
The road out towards Larnaka is grim - busy and undulating - and it's difficult to avoid. I'm glad I went to Cyprus but in the end I decided there were much better places to cycle. Of course hiring a car would give you a lot more flexibility.
