Hi again, lexmann,
As you can tell from my previous response, I'm a budget traveler. But I can recommend three restaurants in Edinburgh that won't break the bank:
The Canny Man's, on Morningside Road. This is a quirky place, with lots of tables in alcoves, and some wonderful sandwiches. You can check out their menu and history on line.
The Merlin, also on Morningside Road. This place is similar to an American sports bar, but Edinburgh style. You don't want to eat there if there is an important (i.e.: Scottish) football match on the telly. They have some two for 10 pounds 99 meals, which would be a good opportunity to try haggis. It's surprisingly not half bad! The Merlin is part of a chain owned, I think, by Belhaven. They have other restaurants in Scottish cities (not all called The Merlin).
Henderson's Salad Table, 94 Hanover Street. Excellent mostly vegetarian restaurant, with a great selection of soups and salads. They have gotten a little more pricey over the years, as they have become more well known, but they're still good value.
In Glasgow, as we're usually staying with friends, we don't eat a lot of meals at restaurants. However, when we take our friends out to thank them for their hospitality, we always go to Cafe Source, which is in the basement of St. Andrews Church, at 1 St. Andrews Square. Their Cullen Skink is excellent. It's a fish chowder. Their traditional Scottish food is also excellent. As with all of the above, they have an on line menu. Check the a la carte menu, not the prix fixee menu.
Most Scottish restaurants have a menu posted in a window or on the door, so you're not faced with sticker shock when you are handed the menu!
You can also get great meals at decent prices at many of the Chinese and Indian restaurants which can be found in just about every city, town, and village in Scotland. The portions can be huge, so ask before ordering, as you may want to share a meal. Rice, whether it be boiled, fried, or basmati, is usually a separate item, so take that in to consideration when ordering.
If you mix budget meals with the occasional restaurant meal, you should be able to eat well and heartily on a budget. My wife and I just returned from 30 days traveling about Scotland, and only once did we spend more than 20 pounds in a day on meals. We do split main meals, however, as portions in Scotland are much larger than they used to be.
Happy travels, and bon appetit!