Gota Park is a stunning, Western Style Park close to Gora Station, which is definitely worth a visit during your stay in Hakone. Here you can find a rose garden, a huge fountain, a craft-house where you can try some pottery or glass blowing (costs of these activities range between 1000 and 3000 yen) and there are also greenhouses in which you can see all kind of different tropical plants and flowers. Gora Park offers a great view of the nearby mountains and will make you realize just how stunning Hakones nature is.
Gora Park is just about 5 minutes walking distance from Gora Station. Entry fee is normally 550 yen, but will be free if you have a Hakone Free Pass. Hakone Free Pass is a affordable voucher that allows you to use most of the trains, buses, rope way, sightseeing boats and more for free. I really recommend buying the Free Pass, it will save you lots of money and time. You also get discounts and free entry to other sightseeing spots around Hakone.
Official website for the Hakone Free Pass (in English): http://www.odakyu.jp/english/deels/freepass/hakone/
Official website Gora Park (in Japanese and English): http://www.hakone-tozan.co.jp/gorapark/