Deirdre's flat is very nice, very clean and very comfy. Just enough space for two, a spacious bedrom, living room and with a renovated bathroom and a small but well-equipped kitchen. Highly recommended!
The flat is not exactly central, but about 15 minutes walk from the tram from the airport (just take it from one end of the line to the other, York Square). About 20 minutes walk to the centre of Edinburgh (Waverley train station). There's both a large tesco and an organic Real foods shop nearby. A small hint for the buzzer on the door: it's button 1F2.