I stayed in Richmond Place with my girlfriend for two nights. The location is very central which was the main reason why I booked this. The apartments are self catering but they do supply you with everything that you would expect from a standard three star B&B (fresh towels, soap etc). Please note that this place is run by the University of Edinburgh and the whole building except one Floor is used as student accomodation. So please don't expect a hotel or a B&B atmosphere. As almost everywhere in Scotland, the outside of the building compley looks a bit shabby and dirty. The interior is like all the University buildings in town. The third floor where the apartments are located is not different. Finding your way is rather complicated. There is an elevator to bring you to the third floor. However, on the third Floor, there are further stairs to go up/down. You better be good per foot, otherwise this could be complicated. The halls are very narrow and claustrophobic. The room itself was a positive surprise. Note that we had the highest category of room. It looked as it had only been used a few times. Very clean (for Scottish standards), all appliances worked (also a bit surprising for Scotland). There was a small couch, The bed was on a mezzanine Level, all in all enough room for two people.
Also important for late arrivals: They have a 24h check in!
I would recommend this to everyone whose primary objective is a central location close to the University and to the Royal Mile.