Taormina is a small hill town with one outstanding asset, a Greek theatre framing Etna, and it works best as a base for the volcano and the gorges rather than as a week on its own.
Teatro Antico di Taormina
A Greek theatre rebuilt by the Romans, cut into the hillside so the ruined stage frames Etna and the coast behind it. It is also a working summer concert venue, so sections can be fenced off for stage builds; go early in the day for both the light and the crowds.
Isola Bella
A small island nature reserve joined to the shore by a shingle bar, in the bay below the town. Get down by the cable car from Via Pirandello rather than driving; you pay separately to enter the reserve itself, and the beach around it is pebble, not sand.
Mount Etna
Europe's highest active volcano, protected as a regional park since 1987 and covering 59,000 hectares. The usual approach from Taormina is the southern side at Rifugio Sapienza, then cable car and guided 4x4 towards the summit area; access to the upper craters changes with volcanic activity and weather.
Gole dell'Alcantara
A narrow basalt gorge about twenty minutes inland, where the river runs between columns of cooled lava. The Parco Botanico e Geologico on the site covers roughly 100 hectares and has its own lift and stair access down to the river, plus parking, and charges admission.
Castelmola
The village on the crag above Taormina, about an hour uphill on the old path or a short ride on the local bus. There is a piazza, a ruined castle and a view straight back down over the theatre; it is free apart from what you drink.