It is possible to rent a villa or book a room in the hotel or apartments.
The choice of cyprus villas is huge, apartments also exists everywhere and of different type. I like more Holiday Villages.
If honestly some of them are located on suburbs of tourist zones, but everywhere there is a good public transport. The island is covered by a dense network of highways which are supported in a perfect condition; the four-strip motorway connects capital Nicosia to the seaside cities of Larnaca and Limassol.
If you go from Larnaca to Ayia Napa, you will not be able to pass territory of military English base Dekelia. Until now days it was impossible to go round the base Akrotiri through which there is a road from Limassol to Paphos. Today there is a possibility: to go by old road or to round the base by a recently laid modern highway to the north from it. If you pass through the territory of base, remember, that it is a sovereign zone. Here operates English laws, and if you made something illegal or crime, you will answer for your actions before English court. The order is watched by English police. On the territories of bases it is not permitted to stop without the essential reason on that and it is not permitted to make video or photos.