One of my favourite shrines in Tokyo is located in Suginami ward, where I live, and is named Omiya Hachiman. It's not that big and as it is in a really suburban area, it is usually fairly quiet, but during big events like Tanabata or New Years it can get fairly crowded. I wouldn't put it up there with other shrines like Hie or Meiji, but it is still a pretty nice place for a visit. In other words, I wouldn't make a special trip to see this place, but if you were to be in the area, it would be worth your while to drop in and see what is there. It is peaceful and has that "shrine atmosphere" which makes it very nice.
I think it is famous for a few things. One is the archery (i.e. Kyudo) dojo which I believe is quite well-known. You can't enter the dojo without permission, but you can watch from near the door if people are there practicing. More of historical interest is that Omiya Hachiman is dedicated to the deity, Sugawara no Michizane, the god of learning.
Look at the ema (the boards on which people write their wishes), and you will see that lots of them will be asking for help with passing exams. And lastly, the shrine also has some quite impressive torii (the big gates found at Shinto shrines). The Suginami Animation museum is very close, so if you are into animation then it is probably a very good place to go to!
Omiya Hachiman also has a lot of mikoshi (portable shrines used during festivals) on permanent display. They are on the left side of the temple, in their own building behind glass. It is nice having them behind glass which makes them easy to see, but hard to photograph, as the windows have mesh all through them.
Omiya Hachiman is pretty extremely easy to get to and is a great place to spend some time especially during one of its larger celebrations. Not only is there the main hall, but several smaller shrines as well which are fun to explore. And it is not too far, about a fifteen minute walk, from Nishi-Eifuku station which is on the Keio-Inokashira line. You can see its (Japanese) website here.
If you enjoyed these articles you could also try:
Inokashira park - one of the most popular parks in Tokyo
Imperial Palace - home of Japan's Emperor
Japan Open-Air Folk House museum - learn a little about Japan's houses of old
Kyu-Shiba-rikyu Gardens - a little park, but a very beautiful one
Sengakuji - the home of Japan's 47 ronin