My bwife and I have visited Edinburgh twice in recent years and just dome the open top bus tours rather than specific photography ones (wife's not a photographer so one would be wasted on her!). These take you round the old town and have a running commentary, although the quality of the commentary is variable - one lady spent around 1/2 the tour telling us how she used to have her milk delivered by Sean Connery and failed to inform us about Grefriars Bobby and a couple of other spots of interest.
The tours we have taken didn't take us out of town at all though and next time we go, we'll aim for Leith as well as the castle etc. Worth being in position at the castle for the 1 o'clock gun in plenty of time to get a good view - get set up and ready then start machine gunning a second or 2 before 1 (using an accurate, correctly set watch as a reference). That way, you should get a shot of the moment the gun actually fires - unless some little scrote elbows you in the back at the crucial moment...
The stained glass saints up at St Margaret's Chapel are rather pleasing shot from inside - again, chose your time and avoid elbows! Shame there's no photography allowed in the war memorial - the dangling sculpture would look great shot from below with a wide angle. Too much respect for the place and sentiment to ignore the signs.