We were in Taormina for 3 nights in 2015. On our first partial day, we visited the public gardens and walked up the hill to a little church with a gorgeous view. The next day we took an excursion to Mt. Etna, which we enjoyed. We were gone most of the day but didn't notice any crowding when returned.
Our final day was Liberation Day, which was a Saturday and it was crazy crowded. Many Sicilians from the countryside visit big cities on this holiday, so it was like a full-day passeggiata, with everyone wandering up and down the street, greeting friends, having huge lunches. We visited the amphitheater early that day, then escaped via funicular to Mazzara Beach (which was almost empty) and visited Isola Bella. That night we attended an Italian Opera performance in a theater on the main square. A tenor, a soprano and a pianist performed 10 arias from various operas. At intermission, prosecco was served on the lovely rooftop terrace. At the conclusion, there was a singalong to Funiculi Funicula. Wonderful experience. And by evening, most of the crowds were gone.
So we had a busy, enjoyable stay in Taormina. There's lots to see and do there. I guess it depends on your travel style. If you are in a place like Taormina or Palermo or Ortigia, you may find some crowding but also lots of options for food, activities, etc. A place like Acireale, in contrast, was empty and peaceful but frankly a bit boring.