Faimous night club in Tokyo is "ageHa"in Shinkiba.You can enjoy several musics and entertainments.If you are lucky,you will meet faimous singer.
For clubbing, ageHa is already mentioned but WOMB in Shibuya is famous, too. (I have never been to either of those... clubbing is not so popular in Japan comparing to western countries)
There are many great bars in Tokyo. "Bar Ishinohana" in Shibuya creates great cocktails. One of their cocktails called "Oribe", matcha latte cocktail, was amazing. They have plenty of original cocktails.
I have heard "bar HiFive" in Ginza is popular to foreigners. I have never been there but my friend from UK said he liked a lot.
If you like whiskey, "bar LIVET" in Shinjuku has a quite nice collection of whisky.