If you would like to use your limited time to visit Hakone, here is suggested itinerary for your reference. Otherwise, I highly recommend to stay at least 3Days/2nights to enjoy fantastic natural scenic and experenice Japan culture by visiting museums and shrines and bathing in Japanese-style hot springs (onsens).
Day One in Hakone National Park
Gentle reminder : Make sure to purchase Hakone Freepass before start your journey to Hakone. All transportation I mentioned below are included in this valuable pass.
Take a pirate boat ride(approx. 30mins) on Lake Ashi to Kojiri-Togendai 桃源台, where is the Hakone ropeway terminal. Then take ropeway to Owakudani 大涌谷(approx. 18mins) - the place offers magnificent views of Mount Fuji and hot springs (onsen) in what is still an active volcanic region.
Had a nice breakfast in guesthouse and checked-out.
Had a morning walk along lakeside to Motohakone. Take Hakone Tozan Bus to Kowakidani 小涌谷,
Yunessun Spa zone: Wearing swimsuit is required. This zone is more family-oriented. There are
25different kinds of spa and water activities, like japanese Sake Sap, Rodeo mountain (water slides), ...
Miro No Yu Spa zone: No swimsuit is allowed. This zone sections into private areas for female and for male and is based on traditional Japanese style including indoor and outdoor bathing facilities. Like Roten Burooutdoor bathing - you can experience an open-air bathing in Japanese garden. You can also enjoy bathing in a unique Taro (a huge wooden bath cask).
Useful link:
Hakone Travel guide - http://www.hakonenavi.jp/english/index.html