Let me ask my friends in Japan. I'll get back to you on this.

-"I think go to some temple or shrine is the best way to feel the Japanese culture. Like Asakusa or other famous temples.And I recommend to eat Japanese noodle 'toshikoshi soba'"

-"Someone local's home. Watch 'Kohaku" and eat noodles with a family would be truly what Japanese do."

My wife who grew up in Japan says that there's tons of parties in Tokyo but if you want to experience it as most Japanese do, follow the recommendations above...