My definition of public place would be somewhere people can walk in freely without specific permission. Open shopping mall is public, whereas closed (after hours) shopping mall is likely not public.
What's your definition of public place?
Wikipedia have definition on public space, but founder said don't quote it without consulting other sources. So the definition there may or may not apply to Singapore.
I regret to say you may end up on a lot of private property and still consider them public places.
Case in point, walk into wheelock place to shoot the inverted cone structure from the inside and you will likely get stopped by the security guard. The building has its management and its own set of rules that one has to adhere to when within its compound.