This question pertains to the USA. In all public universities I'm aware of, anyone can get on campus, sit in on virtually any lecture, and enter the school's library. Does this mean that public universities are considered public space? What about within a public university classroom? Do people have an expectation of privacy when in a public university classroom?
No. Just because some building is "owned by the public" or State, doesn't mean it's public property.
A state's national guard installation comes to mind immediately. State workers' offices are not public places. Airport hangars/buildings/runways. You can't just go hang out in the DPW garages.