Best way of traveling

Hi, My sister and I are flying to Tokyo this weekend. We will be arriving in Narita Airport T2 from where we will go direct to our resort in Hakone. We have not bought JP Rail Pass as we will be staying at our Hakone resort for 7 days after which I will be going to stay in Tokyo for a couple of days before heading back home. We plan to have a restful holiday visiting Mt Fiji and the surrounding areas, hopefully amid the Sakura!
Under the circumstance, pls advise the BEST way to travel around.

Train is a good option...or bus.

I think better to use the train as much as possible is good in order to go to Hakone. The road is much confusion.
Route that I would recommend are as follows.
Riding on the NEX to Yokohama Station or Ofuna station from Narita Airport, Transfer to Tokaido Line at the station either, go to Odawara Station. You go up to Hakone Yumoto Station from Odawara Station through the Odakyu Line. Then you go by Hakone Tozan Line or Hakone Tozan bus from there to Accommodation in Hakone.
It is better to buy the Hakone Free Pass at Odawara Station of Odakyu Line. It is possible ride for two days or three days of transportation such as bus or cable car or train in Hakone Area.
So if you also want to go to Mt.Fuji and Lake Kawaguchi, there is a need from Hakone, go to Gotemba Station, make connections to the bus from there.
http://www.japan-guide.com/e/e5206.html
http://www.japan-guide.com/e/e2358_008.html

Have a nice trip!