Campania, with its stunning natural scenery and impressive lineup of world-class archaeological sites, and historic architecture and art, is in many ways the most all-around well-endowed region of Italy. This is the land of Mt. Vesuvius and Pompeii, pizza and Sophia Loren (both born in Naples), mozzarella di bufala and strong espresso, and the legendary Amalfi Coast. The Bay of Naples envelops in its crescent-shaped embrace some of the most alluring holiday islands in the entire Mediterranean: the legendarily chic Capri, the laid-back spa haven of Ischia, and the tiny villagelike Procida.
Capri and Ischia offer plenty of diversions on their own, but travelers would be wise to combine their Bay of Naples island time with the stellar attractions of the nearby mainland. This is quite easy to do, as there are frequent boat connections between the islands themselves and from the islands to Naples, Sorrento, Positano, and Amalfi. Sailing times are also manageable (the trips between Capri and Naples, Capri and Ischia, and Ischia and Sorrento, for example, only take about an hour), but the process of getting to and from the ports, especially if you have luggage, can eat up a lot of the time. Moral of the story? Don't over-program your days, even if you're staying put on one island.
Many travelers make day trips out of Capri and Ischia, but it's just as valid, if you're in an island state of mind, to do a "reverse commute" -- that is, to use the islands as your base and make a few forays to the mainland to explore Pompeii, Naples, or the Amalfi Coast. From Positano and Amalfi, you can catch a local bus to Ravello and other places along the Amalfi Coast, and up to Sorrento.
Although Capri is visited mostly from mid-morning to mid-afternoon by travelers on package tours or independent itineraries through Southern Italy, it's really best to stay here for at least a few nights: The island is totally different (read: better) when the day-tripping hordes empty out. Despite its diminutive size (10 sq. km/4 sq. miles), Capri has plenty to keep anybody busy for several days, and avid walkers will want to stay for the best part of a week. At 46 sq. km (18 sq. miles), Ischia is a much larger island than Capri and consequently more time-consuming to explore thoroughly; those who come here tend to stay for a few days to a week, though it's perfectly feasible to make Ischia a beach day trip, as Neapolitans often do in summer. Ischia is also the only Bay of Naples island onto which you can bring a car (by ferry only; hydrofoils don't carry automobiles). Having your own wheels is highly recommended here, but the municipal government sometimes limits tourist vehicles in high season -- check with the ferry company before attempting to bring a car aboard.
A geological stepping stone between Naples and Ischia, Procida makes sense to visit en route to either of those places or from the northern Naples suburb of Pozzuoli. It's also possible to get here from Capri directly. Procida is tiny, so unless your objectives include getting to know every fisherman on the island, you don't need more than a day or two here. You might even find that a half-day of wandering around Procida, followed by lunch or dinner and the last boat back to your "base," is quite satisfying.