Asakusa's Sensoji Temple: Tokyo's Most Famous Cultural Landmark
Most people who can only go to Tokyo get their religious-cultural credit by visiting Asakusa. Just head away from the flaming building toward the temple's gate. Called Sensoji, the temple was originally built around 645. It is the oldest temple in Tokyo.
Beyond Asakusa Shrine, you can visit Hanayashiki amusement park or Kappabashi Dori - the restaurant shopping street full of everything you'd need to open and run a restaurant - except food. Asakusa also has restaurants to experience tea ceremonies, eat traditional Japanese food, and try on kimono. Nearby is SkyTree, Tokyo's latest landmark. As with any other tourist destination in the world, do your research on experiences and restaurants as some of them aren't as good as others.
Sensoji's grounds are always open, though the main hall itself is open from 6:00-17:00. Admission is free to everything, though those who visit are generally expected to throw a little change in the box.