Il Latini gets a lot of recommendations from people I know who've been there, mainly just for the family-style experience although I hear the food is quite good too. We tried to go the last time I was in Florence but there were at least 50 people crowded around in the street out front trying to get in, almost all Americans from what I could tell. No telling if that was a unique circumstance or just the way it is (or was).
Lots of people swear by Vivoli for gelato, I thought it was OK but not nearly worth the hype (others clearly disagree). It did look like a good place to get lunch though, they had several nice-looking salads and antipasto in the glass cases at the register, but we just stopped in for a gelato.
We had a nice meal sitting outside at the Caffè Giubbe Rosse in the Piazza della Repubblica, which surprised me at the time because it's a touristy cafe in a touristy location. But we were tourists.