The town with world-famous thermal springs is located 47 km from Naples, which takes approximately two hours by car. Of course, you can take a taxi, but to truly experience the spirit of Italy, it's better to travel by sea.
First, you need to get from the airport to the port in Naples by bus. A ticket for the ALIBUS bus from Aeroporto di Capodichino to Porto (Piazza Municipio) costs 3 EUR (4 EUR if bought from the driver), and the trip takes about half an hour. You can find the bus schedule here. Then, take a ferry or a fast boat to Forio. The price depends on the type of transport (boat, ferry, or speedboat). On average, with luggage, two tickets to Forio will cost between 25 and 50 EUR.