Thanks Rodi. That fills in some key gaps in our knowledge. It confirms my resolve to use the train whenever possible. We will probably take the train from Pompeii to Taormina. (I had already confirmed that the train station is handy to Pompeii on cruisecritic.com)
We have already booked the Schuler Hotel (too bad as there are four of us.) We are also going to a restaurant that the brother of a PV chef runs a couple of blocks from the hotel (La Giara?) where he goes every summer to help out.
Anyway, any other tips that anyone thinks of would be welcome.
Hotel Schuler looks fabulous. It was just a bit too pricey - and we were travelling with kids - so having space and a kitchen was important. The hotel can probably shuttle you up from the Giardini Naxos train station. The hotel has a fabulous overlook of the ocean below.
Are you staying in Pompei or just doing it as a day trip? The town of Pompei is a stop before the one you want if you're going to the ruins. You want the Pompei scavi stop if you're going to the ruins. Wear clothes you don't mind getting dusty - the site is full of ash/dust and we were covered in white dust at the end of the day. The train that takes you to Pompei (both the town and the ruins) runs on a different track than the one run by Trenitalia that take you north to Rome, or south to Sicily... But they're both in the Naples train station - just on a different floor. The whole process of the train being loaded onto/off of the ferry to cross Messina was really neat. And you can go up on deck during the crossing.