Enoteca Alessi is a bit of a hidden gem - just steps from the Duomo but tucked enough out of the way for most visitors to miss. They have a regular series of free wine tastings, and there is one tomorrow from a good producer - Rocca di Montegrossi. If you stop by you can taste several wines (usually 3) and snack on some bruschetta, From 5 pm to 7 pm.
Make sure you also go downstairs to the cellar - they have one of the largest selections of wine in Florence, and uncommonly fair prices for a store in "centro storico" (translation - you are not going to get ripped off here!).
Enoteca Alessi, Via Delle Oche, 27/r, 50100 Firenze (FI), Italy - +39 055 2396987