Meiji Shrine is located Yoyogi, Shibuya-ku.
I went to there by train via Yoyogi station, and the Shrine is near the station.
At New Year's Day many Japanese near Kanto region visit this shrine.
When I visited there, over half of visitors are foreigners.
So there seems to be a famous sightseeing in Tokyo.
I recommend you to go there if you're not particular about your religion.