Florence's most famous and popular market is the aptly named Mercato Centralebut it's by no means the only market in the city. Another ideal spot to pick up picnic supplies, see what's fresh before you browse local menus or simply enjoy the colors of an Italian food market is the Mercato di Sant'Ambrogio (Mercato Alimentare Sant'Ambrogio).
Also known as the Sant'Ambrogio Market, the site is home to stalls that sell many of the same sorts of items seen at the Mercato Centrale—fruits, vegetables, bread, meat, fish, cheese, spices and other sundry pantry essentials. In a couple areas of the market, you'll also find vendors selling clothing and household items.
Because the Mercato Centrale is the more famous market, the Mercato Alimentare Sant'Ambrogio offers a slightly less touristy experience. It's in the historic center, so it's unlikely to be tourist-free, but you may find more locals than visitors browsing here.
The market is located at one corner of the Piazza Ghiberti, due east from the Bargello in the Santa Croce neighborhood. It is open Monday through Saturday from 7 a.m. until 2 p.m. and sits very close to the Chiesa Sant'Ambrogio, in case you'd like to stop for lunch supplies after a morning visit to the church.