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In all of the main towns you can get a community taxi (I think that is what they are called). They have an office where you can book your trip, you share this taxi with other people and it is quite economical. Also there are lots of coach trips to all the interesting places that are quite cheap. The best place to find out about these services would be the tourist office. I think there are bus services between main towns especially during working hours.

You might find a cheap car or motorbike hire but make sure that the insurance is ok. Most of the main roads in the south are very good and they drive on the left. If you want to cross the border go by coach and take your passport.

Cyprus has the worst transportation system! We don't have on a regular basis buses routes and if there are some nobody knows when they start and which are the bus stop, we don't have any trains and we depend only on taxis, or public taxis which takes ages to get you ex from Paphos to Larnaca airport ( 3 hrs when the actually time is 1,5 hrs).

I definitely would suggest to rent a car starting from 25-30 EUR per day, get yourself a nice map and drive around. It is the easiest, the most cost effective and you will safe yourself too much time!

you can try the bus but they are mostly unreliable.

i would strongly suggest renting a car, since indeed the distances are very short. ayia napa is only is 1-1.5 hours away, paphos is almost 2.

alternatively you can ask at your hotel for organised tours across the island.

if you chose to rent a car please remember than we drive on the left like in the UK.

hope you have a nice time in Cyprus:D

I am not from Cyprus but... maybe renting a car would be a nice solution?

Distances in Cyprus are not large either. I remember a Cypriot friend telling me long time ago that you can go from one end to another within 2 hours max.