Check out governmental facilities!
There are cooking classes offered at governmental facilities in Tokyo and Yokohama. These governmental facilities are called "chiku center （地区センター） and hold events to train sports clubs to hold cooking lessons. Although the majority of these classes will be in Japanese, it is worth giving a try to learning cooking lessons from a Japanese person who knows how to make authentic Japanese food. At cooking lessons, they show you how to cook, so perhaps English cooking lessons aren't necessary.
I recommend going to the governmental facility and looking at the fliers on any cooking lessons in the near future. If you need help, you should go to the front desk and say "cooking lessons." They should know what they are talking about.
Cooking lessons at governmental facilities are also cheaper than most other Japanese cooking lessons. Therefore, to get a local experience, learn Japanese and get recipes of tradition dishes, perhaps this is the route to go.