We stayed at Yvonne's flat with a little baby of 4 months for 3 nights. It was convenient as the flat is on the ground floor, so we did not have to carry the pram upstairs. On the other side, you have to take the bus to get to Princes street and other sights -- it was not a problem for us, but other parents need to take that into consideration if they dont want to push the pram around as it will be a longish walk to the main sites.
The flat is very clean and has all facilities for cooking in case you dont want to eat out everyday, which was our case with our daughter. Plus, the flat faces a quiet backyard which is great for silent baby naps. We even had the luxury of sun in Edinburgh so we could open the window to the sound of chirping birds. I highly recommend it.