With a combination of train and public bus from Messina you can easily reach Taormina. A train ride from Messina Centrale to Taormina-Giardini costs € 4 per person (one way) and takes between 40 minutes and 1 hour. In the morning the trains run less frequent than in the afternoon. Check the train timetable before you leave.
How do I get to the train station from the cruise port in Messina?
Messina train station is situated on Piazza della Republica, within walking distance of your docking area. Walk from your cruise ship along the dock toward the ferry terminal. Just before the Stazione Marittima go right. There is the train station.
TIP: In Taormina itself is no train station. Therefore get off at Taormina-Giardini train station. Just outside the station you can take the public bus (Interbus) to the center of Taormina. The journey takes about 20 minutes and costs € 1.80 per person (one way). There run 2-3 buses per hour. Taormina center is pedestrianized. The bus park is a few minutes walk from the city center.