If you're experiencing local music on your trip- assuming you like tradtional or semi-traditional Scottish folk music, which I recommend- a must-go is Sandy Bells in Edinburgh. They have a seisun (session) mostly every day, great bartenders and great food nearby. It's at 25 Forrest Road, not far from the Royal Mile, but also near U of Edinburgh where there are a ton of great and mostly cheap places to eat. If there's a mad Australian with bushy red eyebrows behind the bar, his name is Toby, and tell him I said hi.  

There's a great vegetarian place called Bann's around the corner on Blair Street (the address is 5 Hunter Square). Get the soup. 

 On the east end of town is the Broughton Street neighborhood, more or less the gay neighborhood, so it's naturally where all the good stores and restaurants are. Great place for a walk around and to get lunch. 

 The city has a WEALTH of guided tours through its abandoned  underground (modern E-burgh is built directly on top of old E-burgh), Mercat is among the best, all their people are historians, supposedly (http://www.mercattours.com/home.asp). I go on two or three every time I am there, but beware the scare-factor only tours. Mercat is the real deal. There is a museum through which you can enter Mary King's Close, which is cool, but I would be tempted to check out the Mercat tour since they give one now, also. There are plenty of aboveground tours as well, and some of them are so good, you see locals on them. 

 It has a strange transition from old city to new, like much of Scotland, but Edinburgh is well worth the trip. If you're traveling overland and you're into history, York and the Lake District are well worth a half-day each. It breaks up the trip nicely.