Not living in the Santa Croce quarter anymore, I totally forgot about the Calcio storico which was this weekend. There will also be a match on the 24th, which is the Festival of San Giovanni. On that day there is also a parade (more info), and that night is the Fireworks show at the Piazzale Michelangiolo (website), which I have never seen as we usually leave Florence by June 21/22 (that is when airfare traditionally goes up - the start of summer!).
Also on Saturday night there was the 72nd annual 10k night run - something else I have managed to miss and never had heard of before! There really is just so much stuff that goes on in this town... a good time to be around if you are a tourist.