I had to go to see the tallest tower in Tokyo and the third tallest structure in the world, the Tokyo Skytree. You can take an elevator up and get an amazing view of the city, I stayed on the ground though. There is an aquarium on the 4th floor - Sumida Aquarium that looks worth a visit as well. The aquarium closes at 20.00 (that is 8 pm) so make sure you get there in time. The admission to the Skytree observation decks also closes at a certain time, not open all night.
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