Mountainous Ischia is the largest island in the Bay of Naples, with 20 miles of scenic coastline alternating between sandy beaches and rugged bluffs. At its center is the long-dormant volcano Mount Epomeo, whose verdant slopes are dotted with picturesque towns and planted with a patchwork of vineyards. Ischian beauty spots have served as settings in numerous films, appearing, for example, in the barge scene of “Cleopatra” and as a stand-in for the fictional town of Mongibello in “The Talented Mr. Ripley.” As a result of geothermic activity, the island is renowned for its many spas and hot springs. We prefer to visit outside of July and August, when Italians flock here en masse, causing a surge in pricing for both accommodations and dining.