I don't mean to sound negative, but to me Taormina is way too similar to the Amalfi Coast to make a special trip worthwhile. It would be like "more of the same" because Taormina is Sicily's version of the Amalfi Coast except even more compact (and of course it has the wonderful theater overlooking everything). It gets all the attention and spotlight because it's a jewel of Sicily, but you're already going to the Amalfi Coast (so it would feel a bit repetitive, I think). It took me less than one day to see all of Taormina because it's that small - I could have stretched it out for another full day and gone to the beach and small island below (but I think you get the point).
So if you want to focus on something a bit different than the Amalfi Coast just to "mix it up" a bit, I would consider flying into Comiso Airport (if you can from Naples - it's a very limited airport) and seeing Ragusa and Modica - both wonderful UNESCO sites. Or you can still fly into Catania and easily spend 3 full days in Siracusa which would include seeing the Old Ortygia, the archeological sites and wonderful Paolo Orsi Museum, and a short half day or so side trip to lovely, baroque Noto. Alternatively, you can use Catania as a base to see Mt. Etna which would be a real contrast. While in the Amalfi area, I would definitely recommend not skipping Naples despite all the bad rap it gets (which I don't think is warranted, frankly, but to each his own). I'm very glad I visited Naples and it actually made a strong, bold impression on me that stuck longer than the many coastal towns.
Don't get me wrong, Taormina is gorgeous and worth seeing but I didn't enjoy it as much as I could have simply because I've already been to places that look and feel alike, including Amalfi. Other parts of Sicily gave me a more authentic feel of Sicily, for lack of better words. I loved the whole Val di Noto/Hyblean part of the southeast, including Ragusa, Noto, Siracusa, and smaller towns along the train route.