You might like:
St George at Agios Georgios. Basic meat & fish grills, etc. Great location overlooking the sea.
Seven St Georges, Yeroskipou - gets all the tourist mentions for best mezze in the Paphos area. And rightly so.
Mezodopolian, Yerosskipou - much more of a locals place for a mezze. Good food although not as creative as "Seven"
Viklari - the Last Castle. Google it. Fairly difficult drive to get to it - along a track near to the beach then up a hillside. There's no menu as such. Choice between BBQ'd chicken or pork with p;otato and salad. You'll need to make a reservation - only open at lunch (you really wouldnt want to drive this in the dark) and it gets packed. I just love it....fortunately, the Cypriots drive on the proper side of the road.
The small market at Paphos town is worth a visit to see what's seasonal.