City of Edinburgh council have done good work trialling a segregated path for NCN1 on George Street. Although the trial is coming to an end it's clear from their documents and consultations that George Street will remain the primary east-west route for cyclists travelling through the city centre and more investment is planned.
The problem is that there is very poor access to this route from the West End for any cyclists who have come along Shandwick Place or Rutland Square (including cyclists from the big offices nearby). Heading east, cyclists have to go through the busy West End road junction and then brave cars sweeping into South Charlotte Street as they turn left while simultaneously needing to find a way across two lanes of traffic to the middle of the road to turn right onto George Street -- scary stuff even for a competent cyclist.
Space is always at a premium but there do seem to be options for improving this with minimal loss of road space. A two-way cycle path could be constructed across the paving to link Hope Street with Rutland Place. With careful design this could be done to minimise impact to the pedestrian space and with reconfigured light timings cyclists could emerge from Hope Street to turn left or right, and likewise cyclists from Shandwick Place and Princes Street could turn into the new path. In addition, a left turn strip at Lothian Road onto Rutland Place would provide access to this new path for cyclists from Rutland Square and Lothian Road.