The Name of the Rose by Umberto Eco (1980). Set in a northern Italian abbey in 1327, this novel immerses the reader in the world of medieval Catholicism, monastic life, and ecclesiastical politics at exactly the period when the popes were bouncing between Rome, Avignon, and Viterbo. William of Baskerville's world is the world that built the Papal Palace.
The Etruscans by Massimo Pallottino (1942, revised multiple times). The standard introduction to Etruscan civilisation by the man who did more than anyone to make it a serious academic subject. Pallottino was also responsible for excavating major Etruscan sites in the Viterbo province. Dry in places but essential for anyone who wants to understand what they're looking at in the Rocca Albornoz museum or driving past in the countryside.
Italian Hours by Henry James (1909). James's collected essays on Italian travel, including extended passages on the hill towns and "unknown" cities of central Italy. He visited this part of Lazio and wrote with his characteristic mixture of rapture and exasperation. The chapters on the medieval towns of the interior capture something about Viterbo and its kind that is still recognisable today.