The best way to explore the area is by car., and can recommend a very reasonable car hire company, which I use every time I go to Cyprus, my 2nd home. There are buses in the cities like Paphos, Limassol and Nicosia. There is very little public transport between cities. But there are what's known as Service taxis which are not as expensive as normal taxies and can take up to 8 people. These will travel between main cities and some towns.