I've never been to karaoke with a private bathroom except maybe a love hotel if that counts. In fact I've never seen a karaoke room that doesn't have a window on the door. Of course that hasn't stopped some adult activities.
The big Ferris wheels around town are good. It usually takes 20-30 minutes to make it around. Plenty of time for some fun.
I did enjoy a couple sessions on the rooftop of an apartment building.
I really want to try something in a dressing room at the GAP or someplace like that.
The Ginza cote rooms are very nice! You can't see in the rooms either...very private! No bathroom in the room I used. It's pretty expensive though around 6-7000 yen. We just used it cause we wanted a quicky right away and were drinking next door. The sofa was cozy and the table was sturdy ^^
There are so many accessible rooftops around Tokyo it's almost a waste not to sneak up there for a quickie. Some of them have great views. I recommend against using your own apartment block, especially if your not with your wife!