Not exactly everything.
Most of the privately owned restaurants and bars may be closed around 30 December to 3 January. It really depends on the restaurant/bars so it is very hard to say which one is open and which one is closed. If you have particular places you want to go, you should check if they are open directly to the place.
For shopping malls, museums, sightseeing sights, etc., they are probably open until December 31 and closed on January 1 to maybe 3. but you should check out each of them as well. Some shopping malls and department stores open from New Years Day. Buying a "Fukubukuro", means lucky bag, is kind of a thing to do during New Years. Lots of department stores sell "Fukubukuro" and people line up from early morning to get them. Some Fukubukuro gets sold out very soon such as Starbucks' Fukubukuro.
Shrines and temples are open throughout the year. Actually we have a custom to visit shrines/temples during new years holidays and it is called "Hatsumode". Shrines and temples are a lot more crowded than other times during new years.
Japan's new years holiday is around December 30 to January 3, most of people get holidays during this period.