Nakamise dori Shopping Street has lots of street food. It is a shopping street towards Sensoji Temple, so if you have a chance to visit Sensoji Temple in Asakusa, you will definitely pass the street. There are lots of Japanese snacks, including those limited in Asakusa such as "Kaminari Okoshi" (square shaped rice crackers) and famous "Melon Pan" (melon flavored bread...so good!), etc.
Also, I like Ameyoko Shopping Street in Ueno. The street is always filled with people and small shops. Food there isn't really Japanese, rather international, but most of the street food there is good.
Sugamo Shopping Street is also a fun place. Sugamo is near Ikebukuro, it's northern Tokyo. Sugamo is know as "old ladies Harajuku". There are soft serve, rice cracker, mochi, dango skewers, Melon Pan, etc.
I reccomend "Yanaka Ginza Shotengai" which you can walk from JR Nippori station. You can enjoy Croquette, Ikayaki (grilled aquid), Yakitori and so on. Each food can be taken out so you can enjoy walking the retro street eating those street foods.