The guy who moves to my neighborhood and opens a brothel or biker bar -- even if it's entirely on his property -- imposes real costs on me and my neighbors. In a free society, I have some say about whether I'm willing to accept those costs. Thus, as a member of a free society, I should have legal recourse to prevent him from imposing those costs without my consent. This is an example of how private property rights and community interests may not necessarily be in agreement.
In such cases, property rights must be traded against community interests. We can argue about the parameters of the trade; however, the fact that there is a legitimate trade to be made, is beyond question.
At the very least, this implies a requirement for a legal body with authority to decide between legitimate conflicts of interest, and to enforce the ruling once it's made. Thus, the existence of Chicago property courts is quite defensible, even if their current actions are excessive.
Not to be a hard case or anything but, seeing how private property is the cornerstone of a free society, I only have one question for you. Do you wipe your ass with the Constitution every time you go to the bathroom?
Actually, it is well within questioning.
Your hypothetical brothel and/or biker bar bring up important points.
What is objectionable about a biker bar? Is it the noise? If so, there is no right to disturb the peace.
Is it drunken bikers wandering around on private property? They're not allowed on your property. The only property they're allowed on is the bar's and on the government's property (i.e. the street). In a free society, the government would not own the street - local property owners would and could decide not to allow bar patrons to cross it in order to get to this establishment.
Is it public drunkenness? Again, if you don't want drunks on your property (including now the road) they're trespassing if they do enter it.
Every single objectionable bit of behavior by the bar's patrons is actionable in a free society - i.e. it is a violation of property rights. The patrons would be quiet as churchmice and sober as judges.