Got to agree with Keith on this one,I am a vegetarian and am always most satisfied with my meals at Lokantasi, often "no frills", but always great inexpensive food, and I'm sure if you explain to the staff it is your anniversary they will help make it a special occasion !.
The best vegetarian meal I've had in Turkey was in Kabak in The Olive Garden restaurant, a simple broccoli gratin thing with home made bread, simple but absolutely delicious !, you obviously have to be prepared to travel, or make a night of it by staying in one of their chalets (if they are open then) and this was the view from our table !!.