Why go
The most useful choice is not simply expensive versus inexpensive. Ponte Vecchio concentrates jewellery, central streets focus on fashion, and the Oltrarno offers a stronger connection to workshop traditions. Choosing one area for the kind of object you want makes browsing more focused and leaves time for the neighbourhood itself.
The full story
Begin with the object, then choose the area. Ponte Vecchio is associated with goldsmiths and jewellery, while Via Tornabuoni and nearby central streets concentrate major fashion houses. These streets are easy to fold into a walk through the centre, but they are not the same kind of shopping experience as a small workshop. For handmade-looking objects, cross the Arno into the Oltrarno and explore streets around Santo Spirito and the Pitti side of the river. The area has long been associated with artisans, and the walk gives purchases a clearer local context than a generic souvenir shop. Florentine paper goods, leatherwork and craft objects are common categories, but ask where an item was made and what materials it uses before treating it as local work. Avoid counterfeit branded goods from informal street sellers. If you are comparing quality or price, leave time to visit more than one shop rather than deciding at the first display.