Its all a matter of taste(pardon the pun) but in my humble...
Happy Island is a great place to eat, its closed at the mo but I think its due to reopen at the end of the month. It looks a bit touristy on the outside(erm could be due to them being their main clientele) but the food is lovely.
Sisyfos is also good, reasonably priced too.Plus their desserts come from Morellos bakery and you cant go wrong with a Morellos cake
There are absolutely loads of places to eat here in Paphos so no room to tell you them all. I've tried many of them and cant say I've had an awful meal yet - some fairly unmemorable ones but never a bad one. Trying the Brazilian(restaurant not the wax) this weekend so will let you know if its nice or not.
Happy eating!