The place is amazing! We stayed during a difficult time, arriving only a day after the Queen's passing, so the streets were always full, and late night rehearsals for ceremonial activities made sleep difficult. HOWEVER, the windows open right on to the Royal Mile, and during normal times, I do not think the noise would have been an issue.
The apartment is also huge, with so much space we didn't know what to do with it all! If you like being in the centre of the action, within walking distance to literally every thing, this is the place for you!