The recommended reading depends: if you're just interested in the places you're visiting, I'm sure a good guide book will be enough, especially if the author is Italian. The hard mode (actually very patrician) would be reading The Lives of the Most Excellent Painters, Sculptors and Architects by Giorgio Vasari. The modern classics of art history (for example Roberto Longhi) have not been translated into English yet, so I can't recommend them. Instead, if you want to understand the Renaissance on a deeper level, you should delve a bit into the great Tuscan poets, such as Dante, Petrarca, Guido Cavalcanti and Guido Guinizzelli. Michelangelo also wrote wonderful and tormented poems.
If you're going to hike in the mountains, closer to nature (but in that case I suggest you go up on the Appennines, north and east of Florence) you might read the Orphic Songs by Dino Campana. Campana was a lunatic guy and a visionary poet who died very young. He lived in Marradi, a beautiful town on the Tuscan Appennines, and he used to spend whole days wandering in the woods. His poems and lyrical prose are weird and enchanting.