Palagos restaurant has very friendly and attentive staff. Although they do serve meat and dairy. They do have a vegetarian section on their menu (quite a large selection with curry and mousaka and other dishes). We opted for meza (they have vegetarian option for Greek food too. We had hummus/pitta, vine leaves (stuffed with rice - no cheese), courgette and chickpea fritters, lovely large butter beans in tomato sauce. Tell the staff that you don't want any dairy. Also, the restaurant has a great setting right on the seafront.
Cons: more vegan options