Every third Sunday of the month you can go to a wonderful antique and flea market not far from the central station in Florence.
Next to the big fortress Fortezza da Basso sellers line up their tables filled with all kinds of crazy stuff. Here you can find old books, postcards, watches, cameras, bird cages, furniture (some very beautiful), clothes and much much more. The quality of the goods that are sold here can vary a lot, but the market is lovely, not least since it's located around the artificial lake next to the huge walls of the fortress, so even if you are not going to buy anything this is a great place to take a walk on a Sunday afternoon with friends or family.
Unlike markets in general this one is not too crowded and you don't have to think so much about pick pockets and similar "stuff" which often come along when you go to these places.
Giardino della Fortezza da Basso.