A trip to the Lake Ashi is the default day trip once in Hakone. Actually this is from my point of view the only reason why to come here.
From Gora I took the local bus and for third of the price the other people using more touristic transportation paid for (500 yen vs 1500 yen), I arrived to the lake. From here I purchased a ticket for a round trip with a boat (Pirate boat), economy class, 1930 yen (16 euro). This round trip has two more stops. Between the second and third stop, I preferred to walk, there were just 2 or 3 km, but the views were really gorgeous!! From the third stop I returned to the beginning.
Lake Ashi is a volcanic lake, that was created as a result of an eruption 3000 years ago.
Unfortunately Owakudani (Hot spring place, with steaming ground was closed due to volcanic alert.
Below a map with the local bus infrastructure. The buses were very punctual and for the low price, they offer very good connection to any point of interest.
I found all the buses easy, they have the station names written in Japanese, but also romaji (easy reading for non-japanese).