Must-see place in Tokyo

＊Meiji-Jingu 　明治神宮  - Shinto shrine

A map of Meiji-Jingu is here.

Meiji Shrine (明治神宮, Meiji Jingū), is a Shinto shrine in Shibuya, Tokyo, that is dedicated to the deified spirits of Emperor Meiji and his wife, Empress Shōken.[1][2] The shrine does not contain the emperor's grave, which is located at Fushimi-momoyama, south of Kyoto.

Wikipedia

I recommend you to go into this shrine from the 1st gate "Ichi-no-Torii" next to JR Harajuku Station. 
Before I moved to the U.S., I went to Meiji Shrine and prayed for my family and myself to be well. Whenever I go to Meiji Shrine, I am always filled with a sense of holiness.
You can refer to the article about "etiquette" when visiting the Shinto shrine. Every Shinto shrine is a place that welcomes all, and you can visit the shrine without strictly following this etiquette, but you will feel better about yourself if you follow it.

＊Senso-Ji　浅草寺  - Buddist Temple

Sensō-ji (金龍山浅草寺, Kinryū-zan Sensō-ji) is an ancient Buddhist temple located in Asakusa, Tokyo, Japan. It is Tokyo's oldest temple, and one of its most significant. Formerly associated with the Tendai sect of Buddhism, it became independent after World War II. It is dedicated to Kannon, the bodhisattva of compassion, and is the most widely visited spiritual site in the world with over 30 million visitors annually.[1][2] Adjacent to the temple is a five-story pagoda, the Asakusa Shinto shrine,[3] as well as many shops with traditional goods in the Nakamise-dōri.[4]
The temple has a titanium tiled roof that maintains the historic image but is stronger and lighter.[5]

Wikipedia

Senso-Ji is a top-rated destination for tourists from outside Tokyo.
First, enter through the "Kaminarimon" as in the photo above and walk down a "Nakamise-Dori," lined with shops selling uniquely Japanese foods and sundries, to reach the Senso-Ji grounds.
After you satisfy at Senso-Ji, enjoy the streets around it that remind you of the historical mood of Japan. There are many delicious restaurants and attractive shops, so I recommend you research beforehand.