Ignore the inevitable reverse snobbery further up the thread, Edinburgh's great, but we just like people to wash occasionally (which is what the weegies above complain about).
Pear Tree worth a shout
The Globe on Niddrie Street
Malones (both of them, Leith and Haymarket)
Platform five is ok
Belushis is good too, bit chain-y
Black Bull in the Grassmarket
Grovesnor on Shandwick Place
Scotts, The Queens Arms, Milnes, Amber Rose on or around Rose Street
The Chanter on Bread St, Innis and Gunn tap room on Lothian Road
Angel's Share is meant to be good if you're looking for something posher