There are a few places in Ngo Huyen St. (near Nha Tho Lon (The Huge Church) in Nha Chung St.). The price is reasonable but English songs almost are old and classic ones.
But if you have a hi-fi stereo equipment at your home, you can enjoy without finding any karaoke place.
http://www.amusicalbox.com/
There are a lot of popular songs available, and you dont have to sign up.
Cheers,
Van Thanh Bui