Rick now has a guidebook for Sicily, which would definitely be worthwhile for you. Although I don't always agree with the places he identifies as top sights, my tastes are odd; I think he does a really good job of highlighting the key places of general interest.
It sounds as if you're planning to spend just a bit over a week in Sicily. It is a very large island; you'll have to be extremely selective with such a short visit. Given that Sicily is a bit awkward to reach (it's a very long train ride from Rome, so I'd fly), I'd suggest spending all your non-Rome time in Sicily.
What type of sights and experiences are you interested in--churches? classical ruins? other historic sites? food? natural beauty?
I'm tempted to suggest you fly into Catania (the largest airport on the island) and spend your initial two Sicily days down around Siracusa. That area is a great favorite of almost everyone, with the lovely Ortygia district and a number of atmospheric Baroque towns in the surrounding area. However, two days would only scratch the service there--enough for Ortygia and Siracusa, but probably not for side trips.
I am not a fan of Taormina, which is extremely touristy and has high hotel rates, but it is undeniably beautiful, and some people like it a lot. It would be suitable for a two-night stay; I think Etna side trips are possible, and I believe previous posters have mentioned other side trips they've enjoyed while staying in Taormina.
While you're staying in Palermo, you can easily take day trips to Cefalu and Monreale. The Villa Romana del Casale might also be possible, although it will take more time to reach.
There are many other points of interest in Sicily, and quite a lot of sights in Palermo, but we need more info on how much time you'll have available and your interests.