Historical (but still in print)

Chiang Yee, The Silent Traveller in Edinburgh (1948).

A whimsical view of Edinburgh from a Chinese writer.

Robert Louis Stevenson, Picturesque Notes (1879).

Nobody describes the character, topography or weather better.

Henry Cockburn, Memorials of His Time (1856).

A first-hand account of life in the capital during the Age of Enlightenment.

Robert Chambers, Traditions of Edinburgh (1824 & 1868).

Anecdotes of 18th century Edinburgh and the characters who lived there.