The Worst Journey in the World by Apsley Cherry-Garrard — the classic account of Scott's second Antarctic expedition (the one after the Discovery voyage). It is the best companion to a visit to the RRS Discovery: by the time you reach the foot of the gangplank you understand exactly what kind of journey the ship was built for.
Sunset Song by Lewis Grassic Gibbon — not set in Dundee itself but in the Mearns of Angus and Kincardineshire just north of the city, this 1932 novel of farm life on the eve of the Great War captures the rhythms and dialect of the surrounding countryside better than any other Scottish book. Read it before driving the Angus glens.
Like Leaves in Autumn by Eric Eunson — a popular history of Dundee's jute industry and the women who worked the mills. Short, vivid, and a useful read before a visit to Verdant Works.
Empires of the Imagination by Norman F. Cantor — for a wider view, this history of Scottish-Indian commerce sets Dundee's nineteenth-century rise (jute, whaling, opium, marmalade) into the imperial context that explains why a small city on the east coast of Scotland was for a brief moment the richest per-capita place in Britain.
The Beano: The Story So Far by Iain McLaughlin — a celebration of DC Thomson's most famous comic, founded in Dundee in 1938 and still published from a Georgian terrace on Meadowside. Equal parts history and trip down memory lane.