Not sure about Manly but the eastern suburbs are definitely a no go zone (there are clear signs at the beach in Bondi prohibiting any type of 2 line (or more) kite). You can find the signs near any of the major entries to the beach, where it also says things like no glass allowed, no pets allowed etc. Rules or not, just think about it. Bondi and Manly are some of the most popular beaches in Australia for swimming and surfing. In summer there's gonna be heaps of people swimming/surfing and even more people watching. If anything happens you'll not only get in huge trouble yourself, you might even jeopardize the future of the whole sport in Sydney. Is it worth it? Of course not. So it doesn't matter if you're technically allowed to or not, just don't do it. You might be the best, safest, friendliest, accident-free kiter in the world, but if people start riding there more people will and I can assure you that one of those people won't be as safety minded as you are.
We have plenty of spots in Sydney where we're (at least for now) still allowed to kite at. Much better to go to one of those.
More info on spots:
www.google.com/maps/d/viewer?ll=-31.989442,150.79834&spn=8.939741,14.0625&hl=en&msa=0&z=6&source=embed&ie=UTF8&mid=1LA3B1H3pr16pm9y2fVsBWDeL9C8