Whether you are looking for designer clothing, jewelry, leather goods, or antiques you will find it in Florence. But be careful, Florence can be very expensive!
Designer shops like Versace, Gucci, Ferragamo, Prada, and Bulgari are represented along Via Tornabuoni and Via Vigna Nuova. My tip is to avoid the fashionable streets around the Duomo. You will find nice little shops in the side roads of the city, which are less expensive, or in the area around Piazza del Santa Croce and San Lorenzo.
By the way, one of the most famous markets is the San Lorenzo Market in the centre of Florence. Nice fresh food is offered inside the market building and all other things like shoes or clothes are offered on the street market.
Worth a visit, especially on a nice sunny day!