Go island hopping to Procida
Just a 15-minute ferry ride from Ischia, the pint-sized island of Procida is refreshingly tourist-light (except in August, when Italian holidaymakers pack the sandy beaches).
Visit for the kind of irresistible sights that have you constantly reaching for a camera, like pots brimming with geraniums by the roadside and trees laden with Procida's famous lemons.
Don't miss Marina Corricella. One of the most beautiful places on the island, if not the entire Bay of Naples, it's known for gently faded sugar-almond-coloured houses and a harbour where fishermen still sit and patch nets in the sun.
No surprise that the town represented a 1950s Italian idyll in films like The Talented Mr Ripley and Il Postino. Have lunch at Taverna del Postino which celebrates the latter film and is famous for herb mussels or zeppolins, "small zeppelins".
Should you find yourself in no hurry to catch the ferry back to Ischia, think about staying over for a night or two at La Suite Boutique Hotel. This accommodation has a gorgeous garden and is close to several of Procida's prettiest beaches.
Step back in time in Ischia Ponte
Ischia has a chequered history and in ancient times it was colonised by Greeks, Romans, Saracens, Turks, and Aragonese. You'll find some small museums on the island but the main historic reference point is the magnificent Castello Aragonese.
Sitting on a promontory in Ischia Ponte, this medieval castle is a wonder. Stroll its walkways for sea views, then head indoors for some very intriguing architectural features which will undoubtedly be a first for you.
Chief among these is a little room lined with stone seats. Back in the day, these were occupied by the bodies of dead nuns, propped here so the living sisters could visit them and reflect on the nature of mortality.
After that, you may want to order a Campari at the bar up top in the castle, the views are amazing. Or if you want a more in-depth look at Castello Aragonese, it's included in a day tour of Ischia from Naples.