Here is a sampling of things I've purchased on my last trip in September. I think these are the specialties on Ischia:
1. L'Enoteca, at Vittoria Colonna, 270: limoncello (famous lemon liquer-keep this in the freezer at home), mandarin orange jams, and jars of baba soaked in limoncello. The store owner is very friendly and would be more than happy to give you a small tasting of liquers.
2. Le Muse, at Vittoria Colonna,270 Bis: painted ceramic jugs and espresso cups-the also have bowls, serving plates...the whole array. The styles here are really nice, not the ugly painted ceramics you find elsewhere. The colors are natural. My patterns were ivy vines, very subtle with earthy colors.
There are some boutiques and shoe stores. I found the prices higher than in Naples, but the styles were up to date and very wearable. There are many name brand stores here-I bascially just window shopped those.
Also remember, when in Italy, remember to get the receipt! For any purchases however small!