A couple of my favourite restaurants in town are The Apartment Bistro (7-13 Barclay Place, Tollcross, EH10 4HW, allegedly with a web site) and it's sister-restaurant, The Outsider (15/16 George IV Bridge, Old Town, EH1 1EE). They often have several gluten-free options available on the menu. (I've been told that they do not put flour in their sauces.) The food is excellent at both places, and I often find myself trying to imitate some of their recipes.
Another place, just outside of town, is the restaurant at Dobbies Garden Centre in Lasswade (EH18 1AZ). The restaurant has several cafeteria counters with coffee/beer/wine, breakfast, sandwiches, hot meals, and deserts. They claim to offer gluten-free bread for sandwiches for an extra 50p, though when I was there, they were out of out of gluten-free bread, so I can't comment on the quality. They also had Honeybuns gluten-free cookies and cakes, though.
(It occurs to be that you can find Honeybuns cookies at the Cameo Picturehouse Bar, by the way.)
The Kwok Brasserie (44 Ratcliffe Terrace, Causewayside, EH9 1ST) has excellent Chinese food (including some lovely dishes not available in other places), good prices, and has many items on the menu that are or can be adapted to gluten-free. (UPDATE 9/9/11 - their lunch buffet is not gluten-free, but you can still order dishes from their main menu, and they are as always friendly and accomodating.)
A friend who visited Edinburgh recently stayed at the Kildonan Lodge Hotel, and says that one of the hotel's managers eats gluten-free, and so the chef is willing to prepare gluten-free meals. I have not yet had the chance to try it, though.