Impressive Troodos Mountains in the very center of Cyprus are dramatically different from the Mediterranean coastline.
There is plenty to see in the mountains. Many Byzantine churches are located there as well as orthodox monasteries, the largest and most famous being Kykkos Monastery, once the center of struggle for the country independence. Picturesque villages with friendly and hospitable people will offer your special crop, craft, or product for which a place is known.
However, the major interest is nature itself. Rent a 4x4 jeep and spend a day on safari of your own exploring the mountains that are only 30 to 40 minutes from the beach, an easy reach from Paphos.
You will see breathtaking panoramic views, mist and clouds on the mountain peaks, waterfalls, and crystal clear creeks as well as a great variety of flora and fauna. If you are lucky, there could even be a chance to meet Cyprus horned sheep--the Moufflon.