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Mercato di Sant'Ambrogio
Florence
The Sant'Ambrogio Market is arranged simply: fruits and vegetables on the outside, and all the rest on the inside. It's best to show up before noon as many vendors sell out and then pack up just after noon. The best options are obviously the seasonal products, both for the price and variety. Buying at the market will make you save a little if you are on a budget trip, but it is also a tasting experiences as the goods are mostly local products.
You may also think to organize a picnic lunch with some cheese, bread and fruits and find a ark in the surroundings or take a bus to piazzale or surrounding hills. Otherwise you may decide to eat at the inside Trattoria da Rocco - great Florentine specialities.
If these suggestions are not adventurous enough for you, there is a tripe cart (menu options: tripe, tripe sandwich, beer) just around the corner next to the church of Sant'Ambrogio (Chiesa di Sant'Ambrogio).
This is not a souvenir market, but it makes a nice place for some photo shooting!
Open 6 days a week, rain or shine. Busiest on Saturdays.