How does that look?http://www.fiesta-roppongi.com/
This place in Shinbashi is a Karaoke bar specializes in English songs:
English Karaoke Bar Bruce
The website says they have the collection of 37,000 songs!
The area Shinbashi is said to be "the city for salaryman", thus there are many drinking bar, pubs, and Izakayas you would never get bored. Shinbashi is a walkable distance from Ginza, too. Very interesting area to explore :)