Places to visit at Christmas

+1 Vienna market: take the train so you can try the hot vine, but don't miss the Budapest equivalent either :-) Or the one in Szentendre...

A famous volunteering opportunity is "Mikulasgyar", Santa Claus Factory: http://www.mikulasgyar.hu/
It's about collecting donations and packaging them into Christmas gifts to the needy.

Christmas is mainly a family thing though, visiting relatives and eating Bejgli.
All the public partying is at new years eve :-)

There is one custom though, albeit a little meta by now, called "Betlehemezes":
People dress up as shepherds dressed up to perform a nativity scene, think play-within-a-play in Midsummer night's dream.
They go door-to-door to sing and jest and earn a slab of bacon or a strand of sausage. The village I lived in had a great folk-dance group, I don't know how much this is done elsewhere anymore.