When tourists from abroad go to a shrine in Tokyo, they like to choose Meiji Jingu (明治神宮）near Harajyuku Station(原宿駅）. This shrine, which is dedicated to the Emperor Meiji, is recommended because it is called “power spot” that mean a holy place. My wife’s relatives are working as a shinto (神道) priest.
Another shrine I dare to recommend is Kanda Myojin）（神田明神）, which is dedicated to Taira no Masakado（平将門）.
This shrine is so small that you can walk around easily. And you can find the Edo period’s life in many soba（そば、蕎麦） restaurants and kanmi dokoro（甘味処）around there.
One of my most favorits kanmi dokoro in Japan you can find easily in front of entrance of Kanda Myojin is Amanoya（天野屋）. This shop is famous for Amazake（甘酒） made by koji,malted rice, Also they have a tea room beside shop. Inside you can find many ancient objects like an antique shop.
I always take Anmitsu(餡蜜）there.
When you use a rest room beside a tea room, you can enjoy a typical small Japanese Garden in a house.
Of course, if you go to Sensouji(浅草寺) at Asakusa（浅草）area, one of the most popular temples in Tokyo, you can find this kind of stores, and also enjoy river cruise on Sumida river （隅田川）to Hamamatsuchou (浜松町) area.