Mr Moonlight,
we have the same situation and after trying several reataurants with samish menus found "Tailors restaurant".
This is not a veggie restaurant but the lady owner will cook you a veggie meal if you let her know the day before.
A word of warning, she will NOT cook things like egg and chips!
Its all very plain simple food.
If you haven't been to kalkan before this is were to find it.
From the main street with the post office on your left, walk down the road untill you come to a sharp right hand bend and Tailors is on the left of the bend, it's only about 4/5 tables in an alleyway.
Called Tailors because her husband makes shirts etc upstairs.
Feel free to pm me for more info and I think I have a pic somewhere that I can e-mai.
Having said all that most of the restaurants have veggie options on the menu.
hope this helps
del949l