I would also definitely spend less time in Tokyo and more time around Kyoto and Nara. While you're in the area, you may also want to head to Hyogo prefecture and stop by Himeji and its World Heritage castle.
I don't know what kind of traveller you are, but that seems to me like a VERY high budget trip to Japan. Especially since you don't seem to take into account the cost of your meals, which can be pretty expensive, depending on where you eat.
In my five years here, the best stays that I've had were in Roykans and Minshukus. No need to go overboard either, as long as they're clean, the service usually goes beyond what North Americans and Europeans expect of a hotel without having to pay...
Also, instead of Hakone, I'd settle somewhere in the Fuji 5 Lakes region. Hakone is expensive and there's not much there. And it's also a stone's throw away from
Yamanashi prefecture, known for it's fruit production. They make fairly good wine, too (mainly in and around Katsunuma). It's one of the few prefecture without the ocean as a border.
While you're at it, I hope you plan a stop at an onsen. A trip to Japan without one is just not the same. There are onsen pretty much everywhere in Japan and there are several inexpensive guide like the Lonely Planet and such that mention nice, inexpensive onsen, not usually on the regular tourist routes.
Well, I hope you have a good trip.