There are some great places to cycle in and around Edinburgh. One long time favourite is the Union Canal – great interactive map. It’s FLAT, starts in the centre of town (Tollcross) and goes all the way to Falkirk (though few people get past the Bridge Inn at Ratho).
The edinburghpaths.info web site has been re-vamped bringing together articles about nine routes (7 available as PDF leaflets) and also a large number of local routes created using mapmyrun.com and Google Maps.
Explore the Pentland Hills Regional Park
Routes from VisitScotland (tourist board).
A suggestion from .citycycling
Great selection of routes with maps from John Brewer’s long established site.
Some Sustrans routes PDF downloads Balerno to Bathgate, Penicuik to Dalkeith, Esk Valley.
EdinburghBicycle Routes Page – many throughout Scotland and further south.
More suggestions from bikeforall.net.
Mountain Bike trails in Scotland from britishtrails. (None immediately next to Edinburgh).