Hmm. If you speak Japanese it shouldn't be that hard. If you don't it could be tough?
I think the easiest route would be
1) Find a local community center (Called "Kouminkan" in most municipalities, but often "Kuminkan" within Tokyo -- or sometimes "kumin sentaa" or even "komyuunitii sentaa"). For example, here is a list of Shibuya Ward community centers:
http://www.city.shibuya.tokyo.jp/est/kmkaikan/index.html
2) If you're comfortable with phone calls, call them up and ask if they have a kitchens or rooms for teaching cooking and if so, how to rent them. If phones are scary, just pick the closest kuminkan and wander in and ask. If they have one, they'll teach you how to rent it. If they don't, they should be able to point you in the direction of one that does.
Route B: If you speak little Japanese but your local area has an international center or helpful foreigner's desk at a ward office or something, they might be willing to help you sort out the above procedure. Just tell them you are thinking of teaching a cooking class and heard that community centers sometimes have rooms for teaching cooking but you don't know how to find one.
Neither is elegant, but should work consistently (like a hammer!).
Tw weeks ago when talking about one of the cooking classes someone mentioned kitchens that could be rented at something like "community centers". Could somebody give me some more detailed information or some Japanese webpage on the topic? Friends of mine usually rent a kitchen that is rather small for 20 people and costs 3000 yen per hour.