I would heartily recommend the Wee Palace by the Castle if you are thinking of visiting Edinburgh. My husband and I had the pleasure of staying for our first wedding anniversary and couldn't have picked a better place to stay. The flat benefits from being in an excellent location - you can see the back of the castle from the lounge window. Grassmarket is great for bars and restaurants and just a 10-15 min walk from Princes Street. Flat is stylish, tastefully decorated and spotlessly clean. There is a fully equipped kitchen including washing machine and dishwasher if you prefer to stay in. Sainsbury supermarket 5 mins around the corner. Four poster bed was extremely comfortable. Towels, and toiletries thoughtfully provided. Everything you could possibly need including travel cot and hairdryer as well as Netflix if you are too tired to go out.
Douglas was very friendly and answered my queries promptly. He even went to the trouble of recommending some great restaurants. Nice little Thai just down from the castle.
Our only disappointment was that we had only booked to stay the weekend. I would definitely book here again if I'm ever in the area.