Here's another vote for The Witchery , and it's not that expensive really , getting a table is the hard part.
It has 2 separate restaurants , The Witchery istelf on streel level and The Secret Garden downstairs , you will get a great meal for 2 for under £100 including wine.
Also very good is Guillianos , on Leith walk opposite The Playhouse , I would highly reccomend the Beef fillet on ceasar salad , mmmmmm
Accross the road from Guillanos is Valvona and Crola which Scotty mentioned , now they are expensive but very good , I've onky been there for lunch but a sandwich and a glass of wine was £25 , it was a very nice sandwich but too pricey , having said that there is usually a queue to get in a lunctime on saturdays so they are getting away with it.