This ex UK army firing range provides and area free of the building they seem to be chucking up all over the islands at a rapid rate.
About a mile past Laatchi from Polis turn off to follow the coast to the car park at Aphrodite.
The Aphrodite cave is worth a quick look (its free), swimming around Aphrodite rock is quite pleasant and there's a decent cafe to sit an enjoy the coastal view. From there I'd suggest you either walk or cycle along the coastal path unless you are a serious off-roader. Make sure you take plenty of water as there is nothing beyond this point other than some great coves to swim. (An alternative is to catch or hire a boat from Latchi).
An alternative to turning off along the coastal road is to continue on the road inland and the track it turns into which is driveable to a large picnic area in the woods from where there are a number of roads for the off-roaders as well as footpaths to walk round.