Morningside Road has a few "gluten-free-friendly" places worth visiting.
Cafe Blush (219 Morningside Road EH10 4QT) is a new favourite. The shop serves omelettes, soups, sandwiches and pastries with gluten-free options for all of them. (The pastries apparently come from a place in Marchmont called Madame Bouvy's Tartes.) The shop is light, comfortable (though it can get crowded), and has free wifi. And the food is good, of course.
For Chinese take way, there's the wonderful New Xi'an (101 Comiston Road EH10 6AG). The food is excellent for a carry out, and they explicitly highlight what items on the menu are or can be made gluten-free.
The Zulu Lounge (366 Morningside Road EH10 4QN) is South African cafe, though a bit smaller---"cosy" is the word they use on their site. They'll make sandwiches using gluten-free bread and have gluten-free muffins. They also make red bush tea variants of espresso/americano/latte. Their biltong and avocado salad is also excellent.
I should also mention Loopy Lorna's Tea House (372 Morningside Road EH10 5HS and at the Churchill Theatre, 33a Morningside Road EH10 4DR). I've not yet tried it (the dominant colour pink scares me), but their web site claims to have gluten-free options.
I hope to have longer reviews of these places in the future.
UPDATE 9/9/11 - I have since tried the food at Loopy Lorna's. There are a variety of sandwiches, and they are excellent. Alas, their 372 Morningside Road (at Maxwell Street) location has recently shut down.