Mishima to Hakone to Tokyo in one day

Hi. This coming July we are walking the summit of Mt Fuji and then sleeping in Mishima. On the following day, I would like to catch a bus to Hakone-Machi, and then a boat ride half way across the lake to then take the cable car to the top of Mt Komagatake. Then how would be the easiest way to go to Tokyo, without staying the night in Hakone?
Also, do buses leaving frequently from Mishima station to Hakone? Many thanks, Tiina

Then how would be the easiest way to go to Tokyo, without staying the night in Hakone?

Take buses to Hakone-Yumoto and then the train to Tokyo.

Also, do buses leaving frequently from Mishima station to Hakone?

About one bus per hour:
http://dia.tokaibus.jp/OrangeGuide/pc/table.do?pole=5&busstop=8101&kin...

Thanks Uji san. So we don't need to travel by lake boat? I have googled and is it right that MotoHakone is where the cable car to Mt Komagatake leaves from? And from MotoHakone we take a bus directly to Hakone Yumoto?
Next looking, I am confused about the use of our JR Pass from Hakone Yumoto to Shinjuku. Can we use it all of the way? some of the way? Or not at all?

So we don't need to travel by lake boat?

Using the boat and bus via Moto-Hakone is also a good option, but note that the boat is not covered by the Hakone Free Pass (neither is the ropeway to Komagatake).

I have googled and is it right that MotoHakone is where the cable car to Mt Komagatake leaves from?

No, the ropeway leaves from Hakone-en, which is only served by the boats that are not covered by the free pass. Please see the second map on the following page:
http://www.japan-guide.com/e/e5206.html

And from MotoHakone we take a bus directly to Hakone Yumoto?

Yes. Or all the way to Odawara (every second bus or so goes all the way to Odawara). Alternatively, take the train from Yumoto to Odawara.

Next looking, I am confused about the use of our JR Pass from Hakone Yumoto to Shinjuku. Can we use it all of the way? some of the way? Or not at all?

First you have to go to nearby Odawara by train or bus. From Odawara, you can use the Japan Rail Pass all the way to Shinjuku by using the shinkansen and Yamanote Line via Shinagawa.

Thank you so much. That is all very useful information. Now I can continue with our plans, knowing how that day will run.