My favorite building in Tokyo is definitely the Mode Gakuen Cocoon Tower (maybe just because I watched them build it
?) located near Shinjuku Station, and visible from the Shinjuku Skyscraper District.
It will throw you for a loop should you be lucky enough to see the roof fold open for a helicopter to land!
For cheap sightseeing in Tokyo, just get on the Yamanote Circle Line (green train) at Shinjuku Station, and stay on it until it comes back around. Then you will see most of Tokyo for $2 (perhaps get off at the stop before Shinjuku, or visit Shibuya after and visit the famous crosswalk to avoid explaining to the conductor why you didn't leave the train at all).
http://www.flickr.com/photos/syume/3356601380/
The Tokyo Government Metropolitan Building is also quite significant (the tallest in the photo). Until Tokyo Sky Tree is built, it will have the highest observation point in Japan. It is free! Definitely worth a visit.
http://www.flickr.com/photos/syume/3909658323/
In Roppongi (definitely visit!) we have the Mori Tower - it is one of the tallest buildings in the city, and has an open air observation deck on the roof that offers a terrific view of the area, including the Tokyo Tower!
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For futuristic, definitely visit the artificial island of Odaiba, you will be able to see the Rainbow Bridge very nicely... and they have a statue of liberty replica
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And visit the Fuji TV Building. You can watch free recording of TV show, or visit the observation (in the ball)
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If you make your way to Nagoya (many people skip it, but it is a city worth a day trip at least!) on the way to Kyoto and Osaka, my favorite building is the Mode Gakuen Spiral Towers, right outside Nagoya station.
http://www.flickr.com/photos/syume/3371593169/
It is owned by the same school (yes, school if you can believe it!) as the Mode Gakuen Cocoon Tower in Tokyo.
In Kyoto, enjoy the ancient buildings. There are no tall buildings, other than Kyoto Tower. But you can DEFINITELY appreciate Kyoto Station, one of the largest train stations in Japan. It is in the bottom right of this 360 panorama.
http://www.flickr.com/photos/syume/3258107009/
Make sure to visit Kinkaku-ji (Golden Pavilion), arguably the most famous World Heritage Site (of many) in Kyoto.
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In Kyoto, maybe make a day trip to Nara. It is a magical ancient city, capital city of Japan from 710 - 784. It is said that the former capital cities haven't changed much from the time they were the capital, and, in Nara's case this is mostly true. Many buildings that date back well over 1000 years, and virtually no modern buildings. You can take guided English tour for about $30 per person.
The most famous is Todai-ji home of Daibutsuden (Great Buddha). When it was built in 751, 10% of the Japanese population was employed to build it.
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Inside is the Great Buddha, made of Bronze. For scale, each of the round "dots" on his head are larger than a human head.
http://www.flickr.com/photos/syume/3903090625/
Nara is most famous for its domesticated wild deer population. They are so friendly and let you pet them! This makes it magical
There are thousands of them literally everywhere.
http://www.flickr.com/photos/syume/3903341800/
In Osaka, the most iconic building is Umeda Sky Building (located in Umeda, where most of the skyscrapers are). It has an observation area on the roof, of course!
http://www.flickr.com/photos/syume/3270093075/
Osaka has very interesting architecture, compared to a lot of Japan, it is very modern. A panorama from Umeda Sky Building on a terrible day
http://www.flickr.com/photos/syume/3270918428/
Make sure you visit the Dotonbori area, sample some Takoyaki (fried octopus balls, Osaka is most famous for this!) and go for dinner at Kani Doraku for the best crab in Japan. You can not miss it, it has a giant moving crab on the exterior of the building. It is one of the most famous restaurants in Japan, and actually occupies every floor of the building.
http://www.flickr.com/photos/syume/3271020996/
Everything is crab shaped, even the carrots.
http://www.flickr.com/photos/syume/3356539106/
Maybe visit Kobe in your spare time. It is very close to Osaka! You can sample Kobe beef, not nearly as expensive as in Tokyo or abroad.
Visit Kobe Tower (yet another observation tower) and the Maritime Museum.
http://www.flickr.com/photos/syume/3270823156/
Sorry if I have told more or different things than you cared to know. But, 日本大好きですよ! (I love Japan!)
Have a good trip! Be sure to see many of the historic sites in Japan! If you need help, let me know!