Edinburgh is a great city to visit and Old Town is a great place to stay in if you like history, architecture, literature, or parties :)
A couple of things to be aware of:
1. Location is excellent to explore the Old Town - walking distance to all main attractions, many restaurants and shops right downstairs, you can watch street artists from a window. Not so great to relax - it's on the 2nd floor with windows to the street with restaurants and bars. "Celebrations" usually stop at about 2 am, trucks with supplies roll in and start unloading at about 6 am, and music (yes, bagpipes) plays loud throughout the day.
2. The apartment is managed by a company, not by a person, hence you get "a company" treatment. Chick-in is not bad, you get the keys right around the corner. But the invitation message said we'll get another set of keys in the apartment - there were no keys, send a message, got back "I'll talk to my team", haven't heard in 6 days. Shelves in the frindge were broken - same "I'll get to my team" message. These are small annoyances, so didn't bother us much. A day before departure hot water stopped - we didn't even bother communicating.