Starting with the mountain, there used to be ski lifts going up but while I was there, the lava came and wiped it all out (bummer dude!). I think you can still ski and snowboard (like me) if you want to hike up the thing, but it's quite a hike.
Lots of stuff to see in Catania, but mainly this is the place to go if you want to go shopping, eating, or drinking. There are lots of stores, clubs, kiosks and bars there. My favorite places to go out are Waxy O'Conners Irish pub, and not far away from that, Stag's Head. These are both good social drinking places, I have met people from around the world while drinking Guiness at Waxy's. Have an Erdinger for me at Stag's if you go!
Trapani is on the Western coast of Sicily, a good place to go and relax. Pretty sleepy place if you ask me. Has a nice boardwalk to stroll on just as night falls...
Agrigento is probably the coolest place you can go besides Siracusa, as far a Greek ruins are concerned. The Temples seen at Agrigento are breathtaking, and the Necropolis is equally interesting (if you like dead people).
The Greek Ampatheatre in Taormina is where I saw Jessica Simpson in concert (not that I like her music, but getting sloshed in a Greek Ampatheatre while watching a HOT pop star do her thing? How could I go wrong?!?). It was during Festival Bar, some Italian MTV sponsored thing. It actually was pretty interesting, some of the Italian artists were very good.
Giardini-Naxos is a small place on the Eastern coast. Highlights include a pebble beach where the water is freezing cold no matter how hot it gets. I would book reservations in advance, the place get pretty busy during summer.
The Necropolis in Pentalica is the single most relaxing thing I experienced, oddly enough, while in Sicliy. It also happens to be a bit of a secret to tourists, but since I was there for so long, I was able to coax it out of an Italian friend of mine. Anyhow, it takes a bit of a hike to get down to the bottom, but trust me it's worth it. When you get to the bottom, you will but surrounded by graves dug out of the rock faces all around you, with a freshwater stream cutting down the middle of it all. There is beautiful scenery everywhere you look, and there are even trout in the stream, but you can't fish there.
Alcantara Gorge has the COLDEST water I have ever waded in. I think they have tours and boating, but mostly it's nice to swim in if you have a wetsuit.
I never actually made it to Malta, but most of my friends did. One even got married there. My cousin spent 3 years living there when she was in college, and said it was mostly a tourist trap, so I didn't go. I'm not saying it isn't a good place to go, simply that I don't go for casinos and the like.
Ustica. What can I say to describe to you all the natual beauty the can be seen for a one-and-a-half hour boatride from Palermo? Even pictures can't well describe what I experienced, but I will try. It starts out with the boatride itself. You get on a hydrofoil-style boat in Palermo, and travel for 1.5 hours to Ustica. You will arrive at a dock and walk up a path for about a third of a kilometer, at which point you will see a quaint little storefront-type setting. Here you can find all the stores, eateries, and most of all, scooter rental kiosks. I advise renting a scooter and riding it around the island, it only costs around a day, and you can see the whole island in 2 days. There is a beach with volcanic rocks to go swimming at, with an outstanding photo opportunity-an old lighthouse! See the pictures page for some photos of the beach and lighthouse, my favorite is the one looking up at the top of the lighthouse from the bottom (located in the picture gallery section). They also have camping, or for those not rough aroung the edges, hotels for a modest price.
Everyone already knows what's in Roma, so I will not elaborate here. Go to a travel or information site to learn more, as there is far too much to mention here. I will say this about Roma: Don't eat at the well lit places next to the touristy sights (that means not near the Vatican or Coloseum), they are far too expensive. Find a place that makes traditional Italian food that's off the beaten path and practice speaking that Italian I know you've been brushing up on. In all reality you should find a hole in the wall, this will give you the greatest experience of the Italian culture au natural. The Italians are pretty leanient to tourists if you make an honest effort to speak thier language, even if you butcher it pretty bad. Just keep at it and eventually you will get what you're after.
The Dino and Enzo Ferrari Racetrack in Imola is a place I would suggest for the car buff in you. I only ended up going there bacause they hold annual car shows, and I needed parts for the Bianchina. I saw all types of vintage Italian racecars, motorcycles, and parts vendors. 5 kilometers full of cars, car parts, motorcycles, motorcycle parts, food vendors, and more. I was only able to see 3 kilometers before I thought my legs would collapse. BTW, if you need any parts for Italian cars, I could be of some assistance to you...
If you go to Italy, you need to know what to order. Here is a list of some of my favorite things to drink with food, or just to drink.
Here are some of my favorite brews:

Erdinger is a VERY GOOD German wheat beer,
you will not be disappointed.

Moretti is a popular Italian beer, kinda like the Budweiser of Italy.
I suggest finding a bar/store that sells a version of Moretti called
Baffo d'Oro (it means moustache of gold!), it's a little smoother than it's counterpart.
Baffo D'Oro

Birra Peroni is good to drink with dinner (if you do that sorta stuff),
goes good with hotdogs/hambugers ect.
Tastes sorta like Heineken if you ask me.
Vino Corvo is a good red wine to drink at dinner with red meats, like my favorite-Horse! It is very flavorful, is not dry, and will leave a pleasent aftertaste on your pallete. Best part is it's only like a bottle at the store, and around at a restaurant. Failing Corvo, you should definetly try the house wines wherever you go, you will be pleasently surprized what good tastes you find.