May and June are the best months. The thermal parks and beaches are open, the island is not yet crowded, and the weather is warm enough for swimming from late May. La Mortella gardens are at their best in spring.
July and August are peak season — hot, crowded, and expensive. Ferries fill up and accommodation prices are high. Worth coming if you want the full summer beach experience, but book accommodation well in advance.
September and October offer a good balance: fewer crowds, warm enough for swimming until early October, and the Ischia Jazz Festival (September) is worth timing a visit around.
November through April: Most thermal parks and many hotels close. The island is quiet and cheaper, but services are limited. Worth considering if you want to walk the hills and explore without distraction.