Outdoor views are great, but inside is where it's at!
I was in Florence with a small group of art students, and we spent nearly every evening at Rivoire, and, like the title says, while the view from the patio is breathtaking, I prefer to stand at the bar with the locals. The prices are much lower, and the locals are friendly. If you have the luck to stop by on a night when Luca, head barista and head of the Florentine bartenders guild, is working, you're in for a treat. Luca makes the best [insert cocktail name] (I recommend the Vodka sour, champagne cocktail, and Rossini) in town, all while happily chatting away with patrons, be they florentines of turistas.
I almost forgot, Rivoire's caffe latte and chocolate brioche are a great way to start a day of enjoying Firenze!