IME, there's very little dislocation over the holidays. It used to be if you didn't buy food on the 31st, you're weren't going to eat until the 4th. I flew into Japan on a 744 on Jan 1 quite a few years ago and there were only 4 or 5 people on the plane.

Now days it's totally different, convenience stores, fast food, etc. never shut down, but a lot of restaurants will be closed especially nice ryotei, kaiseki, etc. In fact they tend to close down a around Dec. 26. Museums, etc. will mostly be closed from Jan 1 to Jan 3 as will a lot of retail stores. Department stores are closed just on Jan 1. Public transportation is all running.

End of December/ early January is actually a pretty nice time to be in Japan.
Retail stores and night life is hopping right up until the 31st.
Then it's a lot quieter for the first three days of January but it's fun to visit the shrines and see the shrine goers.