The Book of the Courtier by Baldassare Castiglione (1528). Castiglione spent years at the court of Federico da Montefeltro's son Guidobaldo, and his book is a set of imagined dialogues among the courtiers in the Palazzo Ducale. It is the most influential book ever written about court life, manners, and the Renaissance ideal of the cultivated gentleman — and the rooms it describes are still standing. Read it before visiting the palace and the rooms come to life.
The Lives of the Most Eminent Painters by Giorgio Vasari (1550, expanded 1568). Vasari knew Raphael's circle and his short life of Raphael — born in Urbino and trained in his father's workshop here — is the foundational portrait. The chapter on Federico Barocci, the great Urbinate painter of the next century, is also worth reading.
The Montefeltro Conspiracy by Marcello Simonetta. A non-fiction reconstruction of the 1478 Pazzi Conspiracy in Florence, arguing that Federico da Montefeltro himself was implicated in the plot to assassinate Lorenzo de' Medici. Reads like a thriller and changes the way you look at Federico's serene portrait in the Galleria Nazionale.
The Stones of Florence by Mary McCarthy. Not about Urbino directly, but her chapters on Piero della Francesca offer the best modern writing on the artist whose paintings dominate the Galleria Nazionale.