Hiroyuki's suggestions are excellent. Just try not to squeeze more than one of these into a day. You can easily spend all day in one or two areas of Tokyo as well. Kawagoe is a nice quiet place with a lot of historical stuff to admire.
Kamakura has the daibutsu, but it's a long train ride; I wouldn't recommend it for such a short trip, as you would spend all day going there, walking around, and coming back.
Odawara is a very nice smaller city, and is the gateway to Hakone. They have a great beer hall there with some award winning local brews on tap. Then there's Hakone, which has a whole slew of things to see (check tourist sites)
Yokohama is another major city and is about halfway between Tokyo and Odawara. Tons of stuff there: Akarenga, Sakuragicho, China Town, and a bunch of historically significant spots and great views.
Kyoto has a ton of stuff, and you can easily spend several days there. Temples, shrines, and shopping (oh my!). Kiyomizudera, the Gion district, Ryouanji, Ginkakuji,
Kinkakuji, Arashi-yama, Fushimi
Inari (my personal favorite, and worth spending a whole day for a nature hike). And that's just what I can think of off the top of my head. If you go to Kyoto, you might as well stop by Nara and check out Shika-kouen and
Todaiji. There's also Houryuuji, but short of historic significance it's not really exciting.
The area around Osaka/Umeda station is very lively and interesting, and there are a lot of reasonably priced hotels in the area (and a ton of love hotels!). I also highly recommend the Namba district (where Doutombouri is located) and Den-den town, the Akihabara of Kansai. There's also of course Osaka castle; you should check out at least one castle while you're here, and there's a large one in Osaka (a smaller one can be found in Odawara).
Do a search either on this site or in google to find out about all these places; they're all worth a visit! That should keep you busy