Haneda Airport after midnight to Mt Fuji

In one of the forum, I saw this info, but we are very new to Japan, we do not know what lines are these and how to go about buying the tickets and where are the stations, we need more details, thanks
{From Haneda Airport to Hakone-yumoto Station
By Shinkansen (Bullet train)
Total Travel Time 90min
TOTAL FARE 3,660 Yen
Haneda Airport - (Keikyu Line 25 min. 470 Yen) - Yokohama St. - (JR Tokaido Line 60 min. 950 Yen) - Odawara St.- (Hakone Tozan Railway 15min. 300 Yen) - Hakoneyumoto St}

Shinkansen trains do not operate after midnight. Your best bet is to stay the night at a hotel at Haneda airport and start your trip early the next morning.

http://www.hyperdia.com/en/

To Hakone-yumoto[箱根湯本] last train 23:39 arr from Odawara[小田原] 23:24 dep.
http://ekikara.jp/newdata/line/1402011/down1_10_holi.htm

[Route 1]
http://www.hyperdia.com/en/cgi/en/search.html?dep_node=HANEDA%20AIRPOR...

You have nothing to do when you reach Hakone late at night. Hotel rates in Hakone tend to be higher than budget hotels in urban area(Tokyo, Yokohama or Haneda) .

I don't think your effort is worth it.

Thanks for all the feedback, perhaps, as suggested, we will hang around in the airport for a few hours then take a bus/train to Tokyo (we have not book anything yet) for one night then from Tokyo, to Mt Fuji for two nights and back to Tokyo for another two nights. We have done some research and realized most backpackers or dormitory do not have lift/elevator, I have knees problem, any suggestions where can we book at a budget price of those with lift/elevators