We stayed at the Nira Caledonia and we loved it. It is located in a posh residential area (Stockbridge) close to restaurants, wine/cheese boutiques, as well as the local Stockbridge Market. The area is nice and quiet. The hotel is a series of townhouses with rooms located in both the upper and lower floors. I would highly recommend splurging for one of the rooms with a terrace. Our room was large and had a bathroom, soaker tub, sitting area (with sofa, chair, table), bedroom (king size bed) and then french doors leading to an outdoor sitting area that backed onto a garden....simply divine! The cost of our room was approximately 265GBP and included a lovely continental breakfast in the main restaurant.
We preferred this location (as it was out of the main downtown area of Edinburgh), so you'll need to walk to get to the tourist spots. (Worth noting: it was about 15mins to get from the hotel to the Scottish National Gallery and 30mins to get to the Royal Mile)
We definitely will go back to Edinburgh (one of my top ten European cities) and stay at the Nira again.More