New Years in Japan

Hi so I got a surprise announcement by my parents that we were going to Japan and were looking forward to it but I started reading and learnt new years has a lot of closed places during that period.

How good of a date is December 28-January 4 and are there any suggestions and recommendations in the Tokyo area particularly for January 1-2? If there is somewhere to also show what stores/restaurants are closed and until when it would also be very helpful since they aren't really the planning type and I want them to enjoy the new years even if there is a lot of places closed.