I can't recommend Zoe's place highly enough. The photos on Airbnb don't do it justice as the kitchen has recently been redone but it's a wonderful, beautifully decorated little place that is perfect for a small family or couple.
The kitchen is incredibly well stocked and Zoe is very generous with her provision of towels etc. There are lots of DVDs and some children's toys as well.
We're from the area anyway (we stayed at Zoe's while having work done at our own house) but for those visiting Edinburgh it's a great place to stay - there are very frequent buses to get to Princes Street, the Old Town, New Town etc and it is walking distance from Arthurs Seat, the Meadows etc.