The Blue Bay Restuarant ( NOT Blue Spice, easy to confuse) in Pernera is really worth a look. It is right on the beach, is a bit basic, but the food is lovely. Evenings are always busy, but not so much that they will not find a seat for you. We always go there when in Cyprus, even a couple of times when we were staying in Paphos!!
Viklari in the Akamas Peninsula near Paphos has been mentioned and I would agree, only to be attempted with a 4x4!
If your in the mountains, there is a little tavern in Vavatsinia. Meze like you've never seen.