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Since it's so close, how about Taormina as a base, with a day-trip one day to Syracusa, or Noto and Ragusa. There are several companies in Taormina which specialize in these kinds of outings.
If you are interested in art and architecture, spending at least two days in Palermo makes eminent sense. There are hourly buses from Palermo to Catania, taking 2 hrs. 40 mins. If you want r/r, stay in Taormina. The bus ride to Catania takes 1 hr.