There is plenty of good shopping on the peninsula. Even the smaller villages usually have a few elegant fashion stores, while the bigger ones have an assortment of brand name shops, such as Benetton or Sisley.
More local products consist of woodworks made from the chestnut trees which grow on the mountains in the interior. Some stores also double as workshops, holding demonstrations for groups, showing how much craft is involved in the construction of even a single artifact. One of the better demonstrations takes place at the Notturno factory, just up the way from the central Piazza Tasso in Sorrento. They sell all manner of items as well, ranging from cheap keychains to music boxes to large furniture.
Cameos, small lacquered medallions which have been in existance since the Roman Empire, are also ubiquitous. As with the wood crafts, demonstrations are available, and the larger stores are located in and around Pompeii.
Finally, the Bay of Naples is home to some of the most traditional dishes associated with Italy. Pasta is said to have originated here, as is pizza, so while it might turn out to be impossible to load a few steaming bowls of spaghetti marinara in your suitcase, you can always buy all the necessary ingredients to make it back home from the very elegant food stores in Sorrento, or even from the local grocery stores. No old-fashioned neapolitan dinner would be complete without a glass of Limoncello, a local liquer made from fermented lemon peels, alchol and sugar, and it can be found just about anywhere. It's bottled in every possible shape and size, often with very classy looking packaging, but you can still find tiny stores which display the old rough hewn bottles of yesteryear.