When I was young I used to stay up drinking with friends all night at clubs and bars in Tokyo.
ATOM TOKYO - Shibuya 渋谷
This is popular with young people. I went there several times.
MOTOWN HOUSE - Roppongi 六本木
I like their music choice. I went there several times.
WHAT THE DICKENS - Ebisu 恵比寿
You can enjoy live music and drinking several kinds of YEBISU Beer. YEBISU is my favorite Japanese beer brand. This place is also good for ladies and gentlemen.
WARP - Shinjuku 新宿
It is brand new night club in Tokyo. It opened in October 2018. I will go there someday.
AGEHA - Shinkiba 新木場
I haven't been there yet, but some friends of mine recommend this place.
There are common rules of night clubs in Japan.
However they might be with some exceptions at the respective clubs.
Why don't you go to karaoke after / before night club?
Entertainment Show Places in Tokyo