One option is to take a ferry from Naples to Palermo. We did the reverse--Palermo to Naples overnight. It was great. and I would much rather spend time in Palermo area than Taormina, even though it is beautiful. I think there's probably more things of interest to teenagers in Palermo. You could take a bus to the beach near Palermo one day and Cefalu and Monreale are fabulous. Have a great trip!