Things to do in the rain in Hakone
There are hundreds of galleries, museums, scenic spots and gardens to visit in the area.
We went to the Open Air Museum which has weird sculptures and a Picasso gallery. 
We also went to the Hakone Art Museum - one man's collection of Japanese objects from tea ceremony sets to a steam train! Here, a very enthusiastic and helpful member of staff showed us around the exhibits and let us try on the Samurai battle armour. Here he is with our tour guide, James.
The Tokaido road - 400 ancient cedars still remain on this route used by the Shoguns when summoned to appear before the emperor in Edo.
Took a boat trip across the crater lake of Lake Ashi. Alas, the ferries are dressed up as pirate ships and it rained so hard we couldn't see the shoreline at times.