Piazza della Repubblica
Known as the Mercato Vecchio, this "old market" and its labyrinth of medieval streets and market stalls were torn down in the late 19th century to create the wide, square piazza you see today. Before that, it was the place all Florentines came to buy their food products, set up in little open-air stalls that offered everything from meat and vegetables to spices and oil, along with countless other market goods.
Some of the streets around the piazza still bear the marks of the old market, such as Via degli Speziali, street of the spice sellers, or the apothecaries, who sold mixes of spices and medicines. You can still find one of these "speziali" on nearby Via della Condotta at the shop Bizzarri. Be prepared for being taken back to a past century when stepping into this shop. It's an excellent place to buy interesting spices.
When the market was torn down to create Piazza della Repubblica, a new structure was built in the neighborhood of San Lorenzo to hold the city's food market, the Mercato Centrale. While the Mercato Centrale, or Central Market, is a food market worth exploring, it is a well-trodden path, so this trail will take you to the Sant'Ambrogio market, a slightly smaller but great-quality local market.