The Argumentative Indian by Amartya Sen (2005) — Sen, born just downriver in Santiniketan, draws repeatedly on Patna's ancient history -- on the court of Ashoka, the lost library of Pataliputra, the debates between heterodox philosophers in the third century BCE -- to argue for a long tradition of pluralism in Indian civilisation. The chapters on Bihar's classical past are the best short introduction available.
The Story of My Experiments with Truth by Mahatma Gandhi (1927) — Gandhi visited Patna repeatedly during the Champaran agitation of 1917, his first major political campaign in India. The chapters on Champaran -- written in his characteristically plain, exacting style -- are essential for anyone trying to understand Bihar's place in the independence movement.
Forest of Bliss -- accompanied by John Berger's essay (1986) — Robert Gardner's elegiac documentary of Varanasi has no narration and no subtitles, but it conveys the texture of the middle Ganges -- the boats, the burnings, the early-morning bathing -- better than any prose. Watch it before visiting any city on the river.
Pataliputra by H.C. Raychaudhuri (1958) — A short scholarly history of the ancient city, drawing on Greek, Chinese, and Sanskrit sources to reconstruct what the Mauryan capital actually looked like. Out of print but available in the Khuda Bakhsh library and second-hand online.