Not Shinjuku, but a few months ago I was in Odaiba and had plans to book in for this place on short notice - sadly it was all booked out. https://project-ican.com/en/vr-zone/

Thirdhand, but my friends have told me it is really worth it. Odaiba is known as a popular dating spot - so it isn't hard to believe that they regularly get fully booked out for something new like that.