Try hitting a soba restaurant! We Japanese eat soba noodles on New Year's Eve, wishing for a long life by eating long noodles. Most of the places may be crowded but try hitting one of them and be a local!
I think that restaurants in hotels are open on 31.
But I do not know if they are truly open unless you contact..
Hotel New Otani
And there is a high possibility that restaurants in big cities are open.
Shibuya, Shinjuku, Roppongi, Ikebukuro
I wrote answer to similar question.https://hubjapan.io/questions/how-to-spend-nye-in-tokyo-not-clubbing