It has to do with the Italians as well. The Italians arrived in New York at the turn of the 20th century to see the Democratic Party aligned with the interests of the Irish. So they became Republicans. This tradition has held over the last 100 years, and it is why areas with plentiful numbers of Italian-Americans like Nassau and Richmond Counties are reliably Republican.
Virginian is on the right track. Italians are a strong tradition in the Republican party going back to LaGuardia and continuing through to Molinari and Giuliani. There are also a lot more Jews (@17%) in Nassau County than there are in Staten Island maybe 9% and they vote Dem overwhelmingly. Nassau also has a lot more of the Yuppie environmentalist soccer mom thing at work. Staten Island is more blue collar and from my own first hand experience this group is becoming more likely than their white collar counterparts to vote Republican (at least the last two elections). Perhaps good old Rupert has something to do with that.