Tokyo To Nagoya vis Mt Fuji, Kiso Valley

My Husband & I are planning a trip to Japan in April, currently we plan to spend a few days in Tokyo then on to Nagoya then Kyoto Osaka and Fukuaoka.
We are comfortable with our plans from Nagoya but are struggeling with the Tokyo to Nagoya as we would like to see Mt fuji, experience some of the hot springs there, then on to Kiso Valley and do part of that walk, it looks so amazing. Its been difficult to see how to match all the metods of transport up.
Any suggestions from those who have experienced this

It depends where around Mount Fuji you intend to go? Hakone? The Fuji Five Lake area?

In case of Fuji Five Lakes:
Tokyo - (bus or trains) - Fuji Five Lakes - (bus) - Kofu - (Azusa limited express train) Shiojiri - (limited express or local train) - Kiso Valley - (limited express or local train) - Nagoya

In case of Hakone:
Tokyo - (various options) - Hakone - (buses) - Fuji Five Lakes - continued as above

How to travel to the Fuji Five Lakes:
http://www.japan-guide.com/e/e6905.html

How to travel between Fuji Five Lakes and Hakone:
http://www.japan-guide.com/e/e6905.html?aFROM=5200_6900

How to travel to Hakone:
http://www.japan-guide.com/e/e5206.html