Just spent a great few days re-discovering Edinburgh with my wife and two younger daughters while staying in Lynne's apartment in Rose St. Lynne was very friendly an helpful and provided some great advice for things to do with the kids (Camera Obscura : tick, recommended) and even brought a couple of kids DVDs for them.
The apartment is in the very heart of Edinburgh, perfect for walking to all the city attractions, and everything you might need (coffee, breakfast, groceries, restaurants) is in Rose St or just round the corner.
The apartment itself was very comfortable and has all the modern conveniences such as great wi-fi, dishwasher and washer/dryer.
Highly recommended if you want to stay somewhere that lets you feel the pulse of Edinburgh.