There are loads of great restaurants- from Michelin star places to local bistro type places- it really depends on your budget. The top places would be Kitchin, Martin Wishart, Plumed Horse, (all in Leith) Number One, Castle Terrace, Wedgewood, Pompidour by Galvin (all centre of town) Cafe Cassis, Field, Bia Bistro, Stockbridge Restaurant (edges of town- more affordable than the others). Have a browse of these and their menus and see what takes your fancy. If you are looking for a weekend night in any of these, you would need to book in advance.
La Cucina in the Missoni hotel, beautiful, stylish restaurant and delicious food with Prosecco on draught, what more could you ask? The restaurant in Harvey Nichols is also lovely and has great views. Rhubarb in the Prestonfield Hotel, beautiful room and very good food.