Tokyo during Years End

Konnichi-wa!
Here is my question: As a flight attendant I come quite often to Japan (at least one time a month), so I am quite familiar with the country.
I want to know, if the trains (JR or other local ones) will run through ALL the night from Dec. 31st to Jan 1st - especially trains from Tokyo center to Narita city(because our crew hotel is situated near Narita Airport).I asked already in the Tourist Office in Tokyo, but they were not sure.
And what places are interesting to visit in the night from Dec. 31st to Jan 1st (places where typical japanese New Years celebrations take place).
I was told Naritasan Temple and Meji shrine in Tokyo. Is that true and what other places will be interesting?
Hope to hear from you soon!
Arigato!
Best wishes from Vienna, Austria,
Conny

If you want, you can go hangout with 3 to 5 million people waiting to bring in the new year at Tokyo Tower & Zojoji Temple. The trains do run later than normal, But I don't remember just how much later.