For unspoilt Cyprus, book your hire car and head for the west of the island to Polis/Latchi and the gorgeous Akamas peninsula. It's about 2 hours from Protaras and yes a long way but we have the freshest fish and spectacular scenery.
If that feels like too far, head up into the Troodos mountains - 1 hour or so from Protaras - different terrain and scenery but cooler than the coast. Experience a lunch in one of the mountain villages, tasts some wine or have a coffee with a local. An experience you won't get in the tourist resorts.
For other ideas, see
http://www.cyprus-travel-secrets.com