Corstorphine Hill is a nature reserve and biking is not allowed. People do bike there however and there might be signs of movement - this page suggests that there is a cycling warden who was willing to identify some places where bike stuff might be allowed - i think it is 'the garden'. It has dirt jumps and a loyal band of bikers. Not in town but close by are the Pentland Hills. A recent issue of What Mountain Bike (I think) had a route map, here is another I found online which tells you how to get to the Pentlands form the city centre. Also Pentlands (and so bikeable from Edinburgh) is the Four Reservoir Loop but maybe these (especially the Ratho one are pretty lame from a downhill perspective.