A bit of googling suggests that Tipness won't let you be a guest hamster.
If your height doesn't exceed 175cm or so, how about a cheap twenty-inch folding bike? Order it (with low expectations), receive the package, check that it's set up right, ride it around (and see Tokyo and meet people), give it away. Or, conceivably, decide that it's worth taking back home with you.
Possibly, some of the models are designed for taller people, but I very much doubt it. People 185cm tall aren't rare in Japan but bike manufacturers like to pretend that they are.
If you want more exercise than a cramped little wallmarty bike can provide, consider swimming. You don't have to be a member, and you're sure to find Japanese swimming pools a memorable experience, emoticon.
Thanks for your replies. Tried Tipness (Shibuya) and they do accommodate short term visitors. Pretty good set up eg HRM provided though its best to check whether its the kind of class you are looking for in advance (eg aerobic base, endurance, strength, interval etc)
You can also try Gold's Gym - I was running the Spinning classes in the Yokohama gym but due to other coaching responsiibilities I had to hand them over to another coach.... I know in Tokyo they have some classes as well.