I always favor train travel over air travel when it's convenient (and often faster). But when the train times hit about 3.5 to 4 hours, the time you save by being transported to a city center on the train evaporates--and taking the plane looks mighty good.
Our map below shows the major airports in Italy. Zoom in to see the airport's relation to the city center.
Notice that there are a lot of major, international airports in Italy, a country that's about the size of the state of New Mexico (See: How Big is Italy?)
If you are arriving in Italy from the US, chances are you will be arriving at either Rome Fiumicino or Milan Malpensa. If you are leaving from Fiumicino, you might use the link above to check out the activities in the area around the town of Fiumicino on the coast.
Omio allows you to check public transportation options to your desired destination. It's set to display train information, but once you search you can also find bus and flight options at the upper left of the results screen.
To check on cheap flights to, from or within Italy, CheapoAir might help:
Ferries were once popular for getting to the islands, especially Sicily and Sardinia. This is becoming less common as Ferry fares have become a bit steep, especially for a family with a car. Today it's often better to fly and rent a car upon arrival, even if you have one at your disposal on the mainland--especially if you are only spending a short amount of time on the island. In the off-season, you'll probably find that taking your car with you on the ferry is a better deal. Check out our night ferry excursion to Sardinia.