Hakone was one my favorite places I visited in Japan.
To get there we took the boat ride across the picturesque Lake Ashi, where we caught one of our first glimpses of Mt. Fuji. After a gondola, cable car and short switchback train we arrived in the hilly, hot-spring town of Hakone.
I really loved our time at the Hakone Open-Air Museum. This was one of my favorite stops of the trip. Opened in 1969, the lovely grounds, with beautiful fall colors, are the permanent home for approximately 120 works by well-known modern and contemporary sculptors including many by Henry Moore. There are also five exhibition halls including the Picasso Pavilion which contains many of his ceramic pieces. This is a must see on your trip!
I also highly recommend the Kaiseki Kadan restaurant at the famous Gorakadan Ryokan. The setting was perfect in a summer home of a member of the Imperial family and the kaiseki lunch was again wonderful art. The hotel, a Relais & Chateaux Property, is really wonderful. It is short drive from the museum.