The first visit to the shrine or temple in the new year is called Hatsumode, and it attracts quite some crowds every year, and I think it is a great way to start a new year in Japanese-style. Fireworks are the standard celebrations in many cities in the world, but in Japan it is mostly a cultural setting at a temple like the one in Asakusa, Senso-ji Temple, where the year begins with offering prayers for a prosperous year ahead. Warm crowds in the cold night of December 31, this is a unique experience to spend the early morning time of the new year.
And don't forget your etiquette!