There are a million things to do. It is a fab place. Taormina is the most touristy part, but it hasn't lost it's character all the same. It is a lovely place, with a nearby beach in Giardini Naxos. There are lots of hotels there too so you should have no problem finding a place. Mt Etna is well worth a visit and you can go on tours from Taormina.
Go to Aggrigento too if you get the chance. The Greek ruins there are breathtaking, and the train journey across the middle of sicily is very interesting too. All the towns in the centre of the island are perched ontop of hills.
There are plenty other paces to visit too. Palermo is polluted, but there are amazing buildings and churches there. Also, some of the volcanic islands to the North of the island are worth visiting. I hear syracuse is worth a visit too. We only had 10 days there so we never got to visit.
The food is great, and in general cheap (I suppose everywhere looks cheap now compared to here!). The wine is great too! Enjoy! I envy you.