I've had a bit more of a detailed look at this.
Really like: The liberal use of "Pedestrian/Cyclist Priority Junction 'Copenhagen Style'" along the length of West Coates and Haymarket Terrace, and the mass of segregated cycle tracks.
I'm not sure why there's a need for the quiet street links (blue line) marked in St Andrew Sq and West Register St if there is a segregated track from St Andrew Sq down St David St and along Princes St to the east. The cobbles in W Reg St might not be too popular, nor might encouraging cycling on it if it becomes part of a bustling/pedestrian area between the St James development and St A Sq/Princes St.
The use of the dotted red line for 1-way segregated cycle track on the map is unfortunate as it isn't as obviously as the other continuous lines on the map and underplays how joined up this route is.
Don't like so much: the twisty, turny route to get from Haymarket Terrace to Melville Street. West Maitland Street/Shandwick Place looks like a much more desirable route, bit I guess the tram alignment has ballsed that whole area up. A confident cyclist may well stay on the main road there, maybe turning left at Manor Place if Melville Street becomes at triumph of urban design (it's possible, especially with the central car parking being removed) and getting from Queensferry Road to George Street isn't too tortuous.
Are people cycling west along West Maitland Street, or is the "trams and buses only" sign being taken literally?
All in all: Good stuff! A strong spine to which a good set of segregated ribs (Dalry Road, Morrison St, Lothian Road, Dundas Street, Broughton Street) could be added in due course.