Welcome to FlyerTalk, aussie_boi!
Yes, I've venture that 24 Kaikan in Shinjuku east is what you're looking for. By reputation, it has the youngest, most in-shape, and most foreigner-friendly crowd among all the 24 Kaikan's in Tokyo. Going on the early side is probably a good idea. Although it stays open around the clock (I think), the subways don't, so you want to be out by 11:30 pm or so. As things get later, you'll find more and more of the crowd upstairs sleeping (some guys even use it as sort of a hotel when visiting Tokyo). I have no idea how early is "too early."