One recommended Karaoke establishment is Karaoke-no-tetsujin カラオケの鉄人. They lend their customers cosplay costumes such as anime characters, maids, Japanese schoolgirl uniforms, and Santa Claus for free!
When I went there, their costume selection was mainly for women but a few were available for men. You can choose only one costume when you are staying there though.
They have a great amount of English songs.
Each group can enjoy Karaoke in a private room. Don’t be shy!
They offer food and drinks. English picture food menu is available.
There are tambourines and maracas in the room.
Probably, some of the touch panels are bilingual. You can change the language from Japanese to English.
Recommended Karaoke chain
http://www.karatetsu.com/e/karaoke/index.shtml (in English)
http://www.karatetsu.com (in Japanese)