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The Oxford Bar in Young Street is known to readers of Ian Rankin's novels as  a favourite haunt of his fictional character Rebus. This has had several media mentions.

The interior of Milnes Bar in Hanover Street, and The Cafe Royal in West Register Street. Milnes, the Cafe Royal, the Oxford Bar and the Abbotsford in Rose Street (not shown) are four New Town pubs particularly known as the haunts of a group of mid-20th century poets who wrote in broad Scots, of whom Hugh MacDiarmid is the best known. Others are shown in the Scottish Poetry Library. There are many portraits of the poets and examples of their work on the walls in Milnes.

The Beehive Inn in the Grassmarket which is the starting point of the regular Edinburgh Literary Pub Tour, highly recommended. Hosted by Mr Clart and Mr McBrain, they give a compelling account of Edinburgh writers.
The Beehive Inn was visited by Robert Burns, although the The White Hart Inn almost next door is better known for its Burns connection, see here.