If you're the sort of person that likes to try local delicacies, then you should get a snack from a 'trippai' (tripe stand). These traditional Florentine stands sell 'lampredottos', or sandwiches with tripe (cow's stomach) for €2.50-€3. It might not sound too appealing, but as the phrase goes 'When in Rome...' (or, in this case, 'When in Florence...'). There's one in Piazza Cimatori, two minutes from Piazza della Signoria.
