One of my favourite places I have ever been is the Aoelian Islands just north of Sicily. You can take a ferry from Milazzo. We stayed in Lipari. They are volcanos at various stages of activity. You can bathe in a volcanic mud bath on Vulcano. You can take a night excursion by boat around Stromboli to see the volcanic eruption. If you have any interest in Geology, these places are vey cool. The beaches are covered in pumice. You can find huge bolders of obsidian and other volcanic rocks you could never find here. After our trip to Sicily, my wife and I wish we never left these islands.
Taormina is definately worth seeing. We stayed in Giardini Naxos which is just down the hill on the coast and close to Mt. Etna.
We flew into Catania from Rome, but stayed there as short a time as we could. We weren't feeling like battling a chaotic Sicilian city. We traveled by bus, train, train, taxi, ferry and taxi to Lipari. When we returned to the big island of Sicily, we rented a car and didn't have any problems. I would be very leary to drive in Palermo or Catania, though.
Syrcusa is not really that great. We went there, and I wouldn't recommend it. Their tourist facilities (hotels/restaurants) are pretty poor and the sites aren't really that great.
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