Religion - Two major religions of Japan are Buddhism and Shintoism
If you are interested in Japanese religious concepts, it is better to visit both Buddhist temples and Shinto shrines. Sensoji temple in Asakusa, the oldest temple in Tokyo, is always crowded with tourists from overseas because of its famous traditional shopping arcade (Nakamise). Still, most of them do not pay much attention to the shrine sitting next to the temple, which shows the syncretism of Shinto and Buddhism. It is one of the keys to understanding Japanese religion correctly.
Talking about a shrine worth visiting, a very famous Meiji Shrine located near Shibuya is raised. It is a typical Shinto shrine, and you can realize the difference between Shinto shrines from Buddhist temples. Being located just next to the famous fashion town Harajuku, Meiji Shrine is always crowded with many tourists from overseas.
If you have come to Tokyo before, you might have visited the above two places. In such a case, I propose you visit Kanda Myojin, which I think is the most opulent shrine in Japan, located near Akihabara. Because a deity of the shrine is for commerce and business, a lot of Japanese companies in Tokyo donate Kanda Myojin. It opened a new communication hall for visitors at the end of last year, where you can buy many exotic Shinto goods or souvenirs.
Another idea is to visit shrines located at the top of the mountains if you are much interested in the Japanese religion and have enough time and physical strength. Mt.Takao and Mt.Mitake, both of which are located at about 1-1.5 hour trip from central Tokyo, are known as their long history of mountain asceticism. Don't you like mountain climbing? Don't worry. You can ride cable railways to go up the mountain. You can enjoy both nature and culture at the same time!
In particular, one of my friend guides is a professional guide for Mt. Mitake. He plans a day tour to Mt. Mitake and Mitake shrine, including Shinto training (waterfall purification, mountain traverse, and meditation). If you are interested in these experiences, I will pass your inquiry to my friend guide (his tradename is Taiyaki Guide).
Mt.Takao & Mt.Mitake