Hakone, a town known mainly for its natural hot spas and gorgeous vistas. Old Timers especially enjoy stopping through here to relive a time when there was no tourism. They also make trips here to enjoy sweet bean and fish cakes. The thing I like about Hakone is that though many tourists visit here, the town has not succumbed to the ubiquitous tourist traps found in many major vacation spots like Hawaii and Thailand. You don't see shop owners trying for force their products on to you, and haggling is almost unheard of down here. I hope it remains that way. That's probably why I keep going there.
Another thing I like about Hakone is that it is so conveniently located. Like so many vacation spots in Japan, Hakone is the most conveniently accessible by train, car, bus, and even for cyclers. If you walk to Hakone from Yokohama it only takes 14 hours, and from Tokyo 18 hours. I'm sure you won't be walking there, but if you do and need a place to recuperate your energy then there're plenty of hot spas.
Aside from hot spas what else can you do? Nothing. The spa is the Hakone experience. I'm sure there's plenty of information out there about what to do and where to go, but like many travel itineraries, they rarely work out the way you had originally planned them, so I don't want to give you a long list of what-to-dos. I do recommend, however, that you pay a visit to Kappa Tengoku, perhaps the most original hot spring in all of Hakone. There're no amenities, it's not pretty, but the water is good. Original because it has never changed and has not modernized. It's located right behind the Hakone-Yumuto Station about a 3 or 4 minute walk.
Another nice thing would be to visit some of the fish cake shops because this food is also the most original delicacy in Hakone. I say original because Hakone doesn't take from other prefectures different fish cake techniques. If you eat a Hakone made fish cake it is authentic! No better fish cake you can find in Japan. Also the bean pastries are original.
As far as other places go, well, they're becoming too touristy. Avoid these places.
I like originality. I have a strong aversion to fusion. Many things in Japan just taste good the way they are.