I would highly recommend Ashlie & Grants place to anyone headed to Edinburgh:
1) Location. I don't think it gets better than this. Literally next door from about anything you want to see ... downtown, historic sites, pubs, food and public transit to the airport.
2) Its actually much bigger than the photos make it look, and REALLY well laid out. Very comfortable for two people.
3) Separate bathroom from the shower. Trust me after a 12 hour flight this helps.
4) Quiet and dark when you want to sleep, despite the prime location
5) Go to the Dragonfly bar downstairs! Great drinks!