one of my favourite places in Italy is the island of Ischia. Make sure to to go there off-season as in Summer the island is run over by tourists. But from November on it's wonderful. You can climb Mt Epomeo (a volcano) or go for a walk in the chestnut-forrests, have a stroll through vinyards and lemon and tangerine plantations, have a picknick on the beach, take a dip in one of the thermal springs, hike up to the lighthouse or go on a shopping expedition in the larger towns. There are two bus lines clockwise and counterclockwise around the island which will take you to all the interesting places, parks, castles, gardens, historical monuments, aqueducts, monastries etc.
Quite a few of the attractions are closed from November to Easter, but there is still a lot left to see and do. And make sure to visit the Giardini Ravino, a privately owned botanical garden specializing in cactei - they have the best Torta Caprese (chocolate-almond cake) in all of Italy!