Mt. Fuji

That would be easy enough to do. Mostly likely, you would get put on a Hikari shinansen to Nagoya and transfer to the slower Kodama shinkansen. Or you would take a Kodama shinkansen the whole way from Kyoto to Odawara.

BUT, there are a few Hikari shinkansen from Kyoto that stop at Odawara.

At Odawara station you would take other transportation (bus, ropeway, train) to go to Fuji-san. Look on the web for info about the Hakone Free Pass offered by Odakyu Railways. That will give you an idea of the transport in the area.

After returning to Odawara station you would then take a shinkansen to Nagoya.

mrwunrfl: Thanks for the useful hints. since I am arriving in Nagoya at 10:a.m., will it be possible first to make a flying visit Mt. Fuji from Nagoya and then reach Kyoto on the same day? I have hotel reservation in Kyoto. Any help will be appreciated.

You must mean that your flight will be arriving at the Nagoya airport at 10AM? Either that or you mean that you will be arriving at JR Nagoya station at 10AM.

When will you be travelling? On a short fall/winter day or a long summer day? If it is the former then you probably ought to just go to Kyoto.

If you are arriving at the airport at 10AM, then you probably won't make it to Odawara until 1PM or 2PM. Going to see Mt. Fuji (up close from across Ashi-ko) involves some travelling from Odawara. I suppose you probably can do it but that would be a bit much.

If you have a JR Pass you could take the shinkansen from Nagoya to Shin Yokohama and then get on another shinkansen to backtrack thru Nagoya and on to Kyoto. You might see Fuji-san in the distance from the left side of the train when heading north to Shin Yokohama and on the opposite side when going south to Nagoya and Kyoto.