There's not really anything in the immediate Edinburgh area that I know of - sure you've got some woodland around the Water of Leith, especially up aroung Collington Dell, and there's Blackford, but they're both a bit limited really - and full of dog walkers. There's always Roslin Glen I suppose, but it's still not great. There's very little in the way of woodland in the Pentlands - just a few small plantations.
Let us know if you find anywhere good!
Never assume that somebody else has got the map.