To read before or during your visit:
The Annals and Antiquities of Rajasthan, James Tod (1829). The classic two-volume account of the Rajput kingdoms by the East India Company political agent who based himself in Udaipur for years. Romantic, opinionated, occasionally unreliable, but the foundation of every later book on Rajasthan.
Indian Summer, Alex von Tunzelmann (2007). Not specifically about Udaipur, but the chapters on the princely states — the Mewar royal family among them — give you the political context for the City Palace and the maharanas' long rearguard action against integration into independent India.
The Last Maharaja, John Lall (1980). A biography of Maharana Bhupal Singh of Mewar, the last reigning monarch before the merger with the Indian Union in 1949. Gives a vivid sense of life inside the palace at the very end of an 1,400-year dynasty.
Tamas, Bhisham Sahni. A Hindi-language novel about Partition violence, available in English translation. Set in Punjab rather than Rajasthan, but a powerful counterweight to the Octopussy version of Udaipur — a reminder of the wider upheaval that the maharanas held the city aloof from.