This is a wonderful place to stay in Edinburgh and I recommend it highly. It's very centrally located, and in a neighborhood full of great (not super touristy) places to eat and drink. There's also a Nando's around the corner if you're just too exhausted to bother. You're less than a 5 minute walk from the middle of the Royal Mile, so you're not far from either the Castle or the Palace of Holyroodhouse. Tesco Express is also just a couple blocks away for groceries.
The flat itself is lovely and very clean, with a modern kitchen and bathroom. The pictures don't do the combined living room/kitchen/dining room justice -- it's a spacious room and perfectly comfortable for 6 people to hang out. The larger bedroom is really quite large, so if you're thinking of using the travel cot for a little one, you will still have plenty of room for suitcases and not feel like you're going to bump into things.
If you're not used to being in an urban environment, don't be put off by the exterior as you approach. Cowgate (which you'll traverse if you're walking from Waverley station) can have a bit of a back alley feel with the backsides of buildings and communal rubbish bins, but we never felt unsafe and there was always lots of pedestrian traffic. Also, since you're on the first floor (that's the 2nd floor for Americans), you will hear street noise. I think it's a highlight, because that's part of being in the middle of a lively city, but if you're a light sleeper bring ear plugs.
Sonia & Chris are wonderful hosts, with great recommendations and lots of information in a handy guide. They're also super quick to respond to questions or concerns and very helpful. All in all a great place!