Reading OP's post is not 100% clear. I would cut thru school property, that is not private. Privately owned Condo complex? No. It is obvious why they do not want strangers there.
But any privately owned land with signs posted saying, "Private Property" is generally "Notice" meaning keep out. In my state, such a notice puts the trespass into a different category and a higher offense than unposted or unfenced land.
I would ask the OP, why do you think it is "Ok" to go onto privately owned property posted as such and consider it "Fair Use"?