Can check out:
Asian Karaoke
Wehntalerstrasse 121
8057 Zurich
Contact Mike (0764706256).

It is like a hanging out place/club that have Karaoke, Disco, Billiard, Darts, Bar and Lounge facilities.
I am not a Karaoke fan, so cannot really tell if it is good or not. Just went once, since I happen to know one of the owners.
I think they charge Sfr10 entry (incl 1 free drink) over the weekend. Normal day free of charge.