Japanese Traditional Music

in Tokyo, there's a restaurant where you can watch Great Shamisen Performance in a Good Japanese food.

Here's the website: http://www.waentei-kikko.com/menu_e.html

It is called waentei kikko.

There's another one called Oiwake, you can find it online.

As for Kyoto, have you hear of the RAN KYOTO? It is live music with dining. https://www.rankyoto.com/
"At RAN Kyoto the sake flows and the music plays. A must see, unique experience"

There's another option, the Taku Taku (ライブハウス磔磔)
Although the website is not really foreigner friendly, you can translate to English with google chrome: http://www.geisya.or.jp/~takutaku/

I hope it helps!