Get to know Taormina on your first day. That means - in no particular order - meandering up and down the Corso Umberto I to get an idea of what souvenirs you might want to buy later, walking up to the Greek Theatre to see the city’s most famous attraction, and taking the Funivia (cable car) down to Lido Mazzaro to while away a sunny day lying on the beach.
Your second day is a perfect opportunity to take a day trip from Taormina to one of the many attractions and destinations in the surrounding area. Visiting Mt. Etna, Europe’s largest active volcano, is a popular excursion - but if the weather isn’t good, you won’t be able to hike up very far or see very much.
Day three in Taormina can be another relaxed day close to the city, or can be a chance to take in yet another day trip destination, depending on where else your Sicily itinerary is taking you.