One of the places to visit for a view of Mt. Fuji. Hakone is a quaint little town with plenty more to do as well. I loved the views of Lake Ashi, and walking along the Cedar Tree Route. Taking the various forms of transportation around Hakone was fun too! Our view of Mt. Fuji was slightly blocked by some clouds but it was still so majestic. I can see why people wrote poems and songs about Fuji-san. She isn't "just a mountain".
How To Reach Hakone
Book Hakone Tour Package
You'll need to set of early so I recommend catching the Odakyu Express Train from Shinjuku to Odawara at 9am (all included with the HFP). From here you can jump on the Hakone Bus to Hakone-Yumoto station followed by the railway to Gora. By now it will be around midday so you might want to have lunch in Gora. If you consider yourself a bit of an adventurous foodie then try the local delicacy of 'black eggs.' Just remember to hold your nose!