How about shaved ice (kakigori) ? Recently, there are many shaved ice specialized restaurants have opened, such as Yelo in Roppongi, and ICE MONSTER in Omotesando. Himitsudo in Yanesen area is a long established shaved ice cafe, where hundreds of people line up during summer!
Respect the atmosphere and watch carefully what they are doing in that particular situation. There is a term in Japanese "read the air" and if you cannot do that, it is considered to be very rude. So, copy what people are doing, and how people are acting.
I recommend Yakitori! It’s a Japanese style grilled chicken. You can find yakitori in most Izakaya. It goes with both beer and sake.
There are many kinds, made by different parts of chicken body, so try variety of Yakitori yourself!
I love tonkatsu!
Wako, Saboten, and Maisen are the three biggest tonkatsu chain restaurants. Their menus are priced pretty friendly, with often giving free refil of cabbage and rice! Their restaurants are in most of the major cities in Tokyo such as Shibuya, Shinjuku, and Ikebukuro. They also h...
One of the most famous Tokyo local cuisine is "monjayaki".
Monjayaki is known as another from of Okonomiyaki, but it has different ingredients and broth. It requires instructions to make, but making a monjayaki is also a fun thing to experience! Tsukishima district near Tsukiji is especia...
If you like sweets, I'd recommend trying ningyoyaki. You'll find ningyoyaki easily at Nakamise-dori, a street you will encounter when you visit Sensoji in Asakusa. It's a doll shaped pancake with red bean fillings.
I'd recommend Marugo in Akihabara. Their tonkatsu is juicy yet not oily and I think theirs are the best! https://www.tripadvisor.jp/Restaurant_Review-g1066443-d1660666-Reviews-Marugo_Tonkatsu-Chiyoda_Tokyo_Tokyo_Prefecture_Kanto.html