We really enjoyed this literary pub walking tour. It's more about the Scottish writers than the drinking and you really need to be interested in or want to learn about Scottish writers. The two actors/guides put on a mini-show in front of several pubs and as they walk through old town. If you can't name any Scottish writers, you probably won't like this tour. We loved it and recommend it.
http://www.edinburghliterarypubtour.co.uk
If you are in Edinburgh during August (the fringe festival), the Voluntary Guides of Edinburgh give free tours from trained docents.
http://www.edinburghfestivalguides.org
What I like about them, is they don't pander to Harry Potter or Outlander tourist stuff. They are very knowledgeable in their facts, so I trust what they are saying is more true than the other commercial walking tour guides. They also do not expect any payment at all.