Tokyo-Hakone-Nagoya

We're a party of four and will be travelling from Tokyo-Hakone-Nagoya. We have been to Tokyo and Nagoya before, but Hakone is unknown to us.

We plan to stay 1 or 2 nights in Hakone. We'd like to keep transportation costs down. But I'm unsure what would be the best way to get from Hakone to Nagoya.

These are the options:
1) train the whole way
2) rent a car the whole way

Distances are long. I recommend to travel by shinkansen. Between Tokyo and Hakone, you could use regular trains instead because it is not a very long journey:
http://www.japan-guide.com/e/e5206.html

If you are four and do not mind a long drive, renting a car around Odawara and dropping it off in Nagoya could be the cheapest option. Drop-off fees for cars vary depending on the company and could make the difference.

Alternatively, you could consider highway buses. Ironically, bus travel from Hakone to Nagoya may be cheapest via Tokyo. If you use an overnight bus, you could also save on a night of accommodation. Willer often has rates around 3000 yen on the Tokyo-Nagoya route:
http://willerexpress.com/

Thanks Uji.

Yes, I did think about the option of travelling from Hakone to Tokyo and then taking the Willer bus to Nagoya. I'd certainly keep that as an option. But I'd like to have a balance between cost and time. If it doesn't cost much more, I'd like the car rental option.

We would likely stay in Ikebukuro when in Tokyo. Is there a reason why you suggested to take a train to Odawara then pick up a car?

The company I work for offers car rental deals with AVIS worldwide. Do you know which Japanese car rental company affiliates with AVIS.

We would likely stay in Ikebukuro when in Tokyo. Is there a reason why you suggested to take a train to Odawara then pick up a car?

Because car rental fees are quite expensive. If you stay 2-3 nights in Hakone, it would likely be cheaper to get around by public transportation than by car; and use the car just on one day to get from Odawara to Nagoya.

The company I work for offers car rental deals with AVIS worldwide. Do you know which Japanese car rental company affiliates with AVIS.

I am not aware of a presence of AVIS in Japan. Here is a list of major rental car companies in Japan (towards the bottom of the page):
http://www.japan-guide.com/e/e2024.html