Just outside the excellent Mercato Centrale is the street called Via dell'Ariento, which eventually merges or runs into the San Lorenzo market near San Lorenzo church.
We walked this street after visiting Mercato Centrale so it was easy to not be that impressed by this street market. Most stalls seemed to sell consumable goods, some clothing items, a bit of leather and some tourist stuff - t-shirts, caps and the likes.
Once you arrive in the main San Lorenzo Market (Mercato di San Lorenzo), there are some better leather, clothes and tourist stands. However, we felt both the Via dell'Ariento was a skip and that San Lorenzo Market was not as great as the tourist guides books often make it out to be.