As far as I know, in the U.S. many people don’t care too much about New Years Eve.
In Italy San Silvestro or l’ultimo dell’anno (literaly ‘the last [day of] the year’) is an institution.
People do big things for New Years Eve, travels, parties. Many people plan crazy activities months in advance. Many people start asking
“Cosa fai per l’ultimo dell’anno?” (‘What are you doing for l’ultimo dell’anno?’)
“Dove vai per l’ultimo dell’anno?” (‘Where are you going for l’ultimo dell’anno?’)
in October or so.
Big classic of San Silvestro:
Cenone. Literally and actually ‘the big dinner’.
At home or at a restaurant.
Any restaurant offers a special meal. It starts late and lasts for ever, with endless courses, because hey, you have to wait till Midnight… and what is better than eating while waiting?
Veglione, literally ‘the big vigil’ the name of the big party, “vigiling” for midnight. Normally with music, dancing and fireworks at Midnight
Festa in piazza (‘party in the square’). In any Italian city there is one in the biggest piazza. With some form of entertainment.
At midnight bottles of spumante start to pop… and being thrown around… everywhere.
Personal favorite? At home, possibly in a quiet place in the countryside, with good friends and good home made food.