It's been a few years since I was in Japan, so your mileage may vary.

As others mentioned, there are several levels of bullet trains - make certain to pick the level you'd like to experience. There are three levels of shinkansen (Nozomi, Hikari, Kodama).

You can use a Japan Rail pass on the Hikari, but not the Nozomi. Purchasing a JR pass in the US cost less than purchasing the same pass when in Japan.

There are a lot of smokers in Japan. I recommend that you reserve seats in a non-smoking car, at least a few days in advance.

If you do the Tokyo to Nagoya route, you will pass Fuji-san. From Tokyo to Nagoya, I remember Fuji in the distance on the right side of the train.

On the shinkansen, snack/sake/beer vendors routinely rolled carts through the aisles. There are snack bars/restaurants in most stations. Nagoya's is part of an underground mall type area.

There's not much room for luggage.

In my travels in Japan I found the english speaking Japan Rail phone number to be invaluable. I've forgotten it, but you may consider calling the NY office of Japan Rail and asking them for the number that you can dial in Japan for assistance in English. The JR website is http://japanrail.com and the NY number is listed there.

I would call them from Nagoya and tell them where I was, where I wanted to be, and they told me exact transfer times. In Tokyo, you'll be fine - many of the signs are in English, In Nagoya many of the signs are in kanji, hiragana and katakana.