Yasukuni Shrine
If you do want to go see what all the fuss is about, then walk from Kudashita station and then up the path towards the shrine. Entrance is free but there really isn’t much to see there.
The best (worst) thing about the shrine is the ugly building erected at the opposite end of the main path, which ruins the view when walking back to the station, away from the shrine. This is why “When Japan” recommends walking from Kudashita Station or from the Tayasu Gate after walking around the East Gardens of the Imperial Palace (map and opening times), which contains the remains of Edo Castle. At least that way you can forget you are in a city for a short while (the best place to do that is actually Meiji Shrine, near Harajuku).
