Hakone and Mount Fuji trip

Will disembark princess cruise at Yokohama on Apr 29 2015
Pls adv the best way and cheapest way to travel from yokohama to hakone on Apr 29. I plan to stay at hakone for 2 nights (Apr 29 and check out May 1) for onsen and view mt fuji
Then from hakone back to shinjuku (staying at New City shinjuku hotel)
Please help me with the transport (yokohama to hakone, hakone to shinjuku) and hotel in hakone.
Seems most of hakone hotel restaurant close early so where can I find food nearby.
Is there any shopping mall with dining at Kawaguchiko train station?

Thanks and waiting for your kind reply

Train would probably be easiest. Put your start and ending destinations into http://www.hyperdia.com/en/ and it will give you some options and costs.

Kawaguchiko looks to be pretty small (two platforms, a waiting room and toilets). Across the street the large building looks to include cafe and/or a 7-11 and a bit further an Italian restaurant (streetview is very handy). Not sure that there is any big shopping nearby.

Apr 29. I plan to stay at hakone for 2 nights (Apr 29 and check out May 1)
Right in Golden Week: transport and accommodation at an absolute premium.
I suggest involving the assistance of a Travel Agent.