If you go right where E709 road ends at Polis, you head down E704 will go through the main part of Polis, then onto a great oceanside road that hugs the coastline. You can drive this around 20km more until you come to a checkpoint into Turkish Northern Cyprus. If you decide to cross over, you will need to have your passport and buy compulsory insurance for Northern Cyprus at the border regardless what coverage you have for Greek Cyprus. There are plenty of great sites before reaching the border so there is no reason to cross unless you are feeling adventurous. My favorite area was a protected marina just a few km before the border. There are lots of designated picnic areas near the water on E704 with picnic tables, chairs and rubbish bins along this road. You can either take the same route back or follow the signs for B7 for a longer drive through the mountains (further inland) to get back to Paphos. Either way enjoy!
We stayed in Paphos on the west coast of Cyprus for a couple weeks and did this drive a few times because it was so scenic... trying out various side roads and routes. This is the winter 'slow' season, but there were still plenty of restaurants and shops open in Polis and Paphos, which is in sharp contrast to the east coast area of Protaras/Agia Napa which basically shuts down during the wintertime.