Bob Meyer: The question I have, which this doesn't answer, is about private property that is effectively a public space, like the outdoor areas of a shopping center. Do rules for a "public space" apply, or rules for "private property"?
Incorrect, it depends on the state. In some states, the common areas of a shopping mall is considered the functional equivalent of a traditional public space and thus, free speech/activity is protected as long as it doesn't interfere with the commercial activity of the mall. California is one of these states. In CA, you would have the right to take photos in the parking lot or even in the common areas inside the mall.