You can travel
by Fujikyu [Fuji Kyuko] from Kawaguchiko to Otsuki (in Yamanashi)
then eastward on Chuo Line by JR-East from Otsuki via Takao to Hachioji (in Tokyo)
then southeastward on Yokohama Line by JR-East from Hachioji to Shin-Yokohama (in Kanagawa)
then on Tokaido Shinkansen by JR-Central from Shin-Yokohama to Nagoya (in Aichi).
The JR leg from Otsuki via Hachioji to Shin-Yokohama looks roundabout, but there seems to be no shorter railroad route to a station on Tokaido Shinkansen.
If you do not take an express train except on Shinkansen, the regular one-way cost is about 13000 yen per adult.
Depending on your itinerary, you may save your cost by using a rail pass / paying a JR basic fare for a longer leg.
(How is the rest of your itinerary?)
Most of eastbound trains available at Otsuki run only to Takao, but some of them run further to Tachikawa, making a stop at Hachioji.
e.g.
Kawaguchiko (08:16) -- (around 09:15) Otsuki;
Otsuki (around 09:25) -- (around 10:15) Hachioji (10:30) -- (around 11:10) Shin-Yokohama;
Shin-Yokohama (11:22) -[Tokaido Shinkansen: Hikari 469]- (13:09) Nagoya.
planning to visit Lake Kawaguchi early of June2014... from here we will travel to Nagoya.. Is there any timetable & booking online link? Maybe it will be already in a rainy season, maybe not yet. Please get ready for rainfall and moist weathers.
http://www.japan-guide.com/e/e2277.htmlTourism in Japan is comparatively inactive in June, so I suppose you can reserve your seats in JR Shinkansen super-express / Ltd. Express trains when you arrive to Japan.
Reservation of seats in JR express trains can be made from one month before the boarding date.
Regarding Tokaido Shinkansen trains, even passengers living in Japan cannot only reserve a seat without payment through a JR website / ticket counter.
Bus and railroad timetables on major lines may depend on whether the day is a weekday or a Saturday / a Sunday / a public holiday.
We will have no public holiday in June 2014.