Shinto Shrines are all over Tokyo. There are estimated to be about 80,000+ shrines in Japan. Over one-third are associated with Inari. That's over 30,000 shrines! These are all really interesting to explore.
The Japanese are incredibly kind and understanding of foreigners but there are a few etiquette rules to keep in mind when visiting a shrine: When you enter, pass through the torii gate. All shrines have a torii gate, even if they do not have a main sanctuary housing the spirit of a deity. A torii gate is the boundary line between holy ground and the secular world. Passing through the torii gate signifies that you have stepped into the domain of the deity. Next, purify your hands and mouth at the water pavilion (temizuya)
Don't drink the water! It's blessed water for you to perform a ritual called "misogi" to purify the body and mind with water before proceeding to stand in front of the deity. In ancient times this ritual was performed in the nude at special misogi locations like the ocean or a river, but today you can get by by simply rinsing your hands and mouth.
The process goes like this: First, scoop up water in a ladle with your right hand and pour water over your left hand. Next, hold the ladle with your left hand and pour water over your right hand. In your left hand, take some water that you have scooped with the ladle and rinse your mouth. Never touch the ladle directly to your mouth. Lastly, using the remaining water, tip the ladle to rinse it off. Once inside the shrine, at the altar, bow twice, clap your hands twice, and then bow once to pray. Toss a coin into the offering box. (the 5 Yen coins are the lucky ones). The coin is an offering to the deity. Ring the bell to greet the deity. (If there is no bell you can skip this step) Bow twice. Clap your hands twice. This clap has the same meaning as a hand clap to express happiness or appreciation. It expresses your joy of meeting with the deity and respect towards the deity. With your hands still together, express your feeling of gratitude in your mind without speaking. Bow one more time.
It might seem like a lot, but while you certainly don't have to do these things but if you do, native Japanese folk will appreciate your desire to follow the custom and be respectful.