Where to visit besides Tokyo and Kyoto?

Great suggestions above but keep in mind 7 days ain't long and there's the travel time between Tokyo and Kyoto so forget anything that isn't one to two hours away from either place or an overnight bus away.

If you take the shinkansen, it will take about 2 to 3 hours to get to Kyoto from Tokyo. Overnight bus will depart at 11:00 pm in Tokyo and pull into Kyoto early the next morning. Won't be too comfortable but you'll save time.

The must-see spots around Kyoto and Tokyo for such a short trip would be:

Kamakura which is only an hour away from Tokyo. There some great temples, beach scenery, and an outdoor Diabutsu, Great Buddha:

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Nikko is two hours away. Has some great mountain scenery with towering cedars and ornate shrines:

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Around Kyoto, Nara, the first official permanent capital of Japan way back in the 8th Century. There's another big statue of Buddha and a huge temple surrounding him. There are persistent deer you can feed in the park.

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If you go to all three that'll leave you about 4 days for Tokyo and Kyoto. I'd do Kamakura and Nara because they're closer to the two cities. Nikko though great and recommended would require 4 hours of roundtrip travel and possibly an overnight stay.

Osaka, Nagoya, and Kumamoto have beautiful castles. Osaka's has been rebuilt and even has an elevator inside. My personal favorite is Kumamoto castle. It had never been overtaken and was the last bastion of old Japan. Kyushu is often overlooked to travelers, but they have hot springs, beautiful scenery and some of the oldest history and best pottery in the country.

Miyajima, near Hiroshima is a beautiful island that is very picture worthy.

those are just a couple of ideas

I would recommend Fukuoka. There is a lot to see in the city. Their aquarium is great. If you can take in a baseball game at Yahoo! Dome, the dome is great to see. Shopping at Tenjin, and the huge shopping center called Canal City. You have to try Hakata Ramen also. Very unique ramen in Fukuoka. Then less than an hour away by local train is KitaKyushu, their natural history museum is wonderful, right next to space world if you are into amusement parks. Fukuoka is probably my favorite city in Japan.

Enjoy your trip.

you should head over to osaka, its near kyoto (personally i'ld rather go there than tokyo)

maybe kamakura if your interested in more history and temples (buy some pigeon cookies if you do go)

hokkaido is nice if you get a chance but its a different island

yokohama area is fun but not necessarily a "must-see" if you're in a time crunch

fuji

Try Nikko...a few hours out of Tokyo...a bit rural with quite a bit of historical stuff.

That's for 7 days! Maybe Osaka if you can squeeze some time.

Okayama, Hiroshima, Matsumoto...well...EVERWHERE!

you can go to osaka. they have lots of nice things there that you will enjoy.

and since you are going to japan, you have to visit mt. fuji!!

Nikko, Kobe, Nara, Hakone... they're all great places! hiroshima too! :)

Go to fuji! (FUJI-KOKO) it is an hour's drive from tokyo anyway!