The Agony and the Ecstasy by Irving Stone (1961) — A fictionalised biography of Michelangelo, covering his years in Florence under Lorenzo de' Medici through to the completion of the Sistine Chapel. Reads quickly and puts flesh on the city's Renaissance story in a way that academic histories don't.
Brunelleschi's Dome by Ross King (2000) — The story of how Filippo Brunelleschi solved the engineering problem of the Duomo's dome — without scaffolding, in a technique he kept secret from his rivals. Essential pre-trip reading; you will never look at the dome the same way after.
The Stones of Florence by Mary McCarthy (1959) — A short, opinionated, and beautiful essay on Florence and its art by a writer who understood both deeply. The best single piece of writing about the city.
The Name of the Rose by Umberto Eco (1980) — Set in a Benedictine monastery, this medieval murder mystery saturated in theological argument and medieval learning gives the period context that explains what you see in the Florentine museums.
The Decameron by Giovanni Boccaccio (c.1353) — Written in Florence in the aftermath of the Black Death, the frame of ten storytellers sheltering from plague in a Florentine villa gives a vivid picture of the mercantile city Boccaccio knew.