Not too strange, but still worthy of mention. The Tokyo Metropolitan Building in Shinjuku.
The top floors are free observation towers.

Something on the island of Odaiba near Tokyo Bay.

Another building on Odaiba.

The famous Fuji TV building. Well I think it's Fuji TV so maybe it's not so famous.

The back of said building.

Not strange, but cool and expensive. The Shinjuku Keio Plaza.

Possibly the most expensive apartments in Tokyo, Roppongi Hills.

The famous Shibuya Crossing, as featured in Lost in Translation.