Travels with a Tangerine by Tim Mackintosh-Smith — Not specifically about the Cinque Terre, but this account of following Ibn Battuta's 14th-century travels through the Mediterranean gives a sense of the long history of the Ligurian coast and its relationship to the wider sea.
The Food of Italy by Waverly Root — An older classic, but Root's chapters on Liguria remain unsurpassed for explaining why Ligurian cooking is distinctive: pesto, focaccia, fresh pasta, and the terraced anchovies that are the Cinque Terre's speciality. Root travelled extensively through the region and his observations are still accurate.
Italian Hours by Henry James — James spent time on the Ligurian coast in the 1870s–1880s and several of these essays describe the experience of travelling by train and on foot along this stretch of coast before tourism transformed it. The contrast with today makes for melancholy but illuminating reading.