Overview
I think it's fair to say that Edinburgh is a bit of a mixed bag when it comes to cycling - a mixture of cycle paths with no traffic (although often covered with shards of glass), roads with cycle lanes and roads with little or no protection for cyclists where some degree of bravery is required. There are also some roads such as the Western Approach Road and of course the Bypass (A720) where no bikes are allowed.
A number of national cycle routes pass through or near the city. Again the quality of these varies a bit in terms of surface and signage - and a number of them make use of the arementioned cycle paths - but they are growing in popularity and in my mind at least are to be recommended.
There are a good series of maps available - created by the local Cycling Organisation, Spokes, which show the locations of the various paths. These are titled Edinburgh, Midlothian, West Lothian and East Lothian. There is a bit of overlap between them, but I would recommend them. They also do one for Glasgow.