Technically there is no right to privacy in public places in the U.S. Constitution. (Hence the distinction between "public" and "private") The closest thing would be the 4th Amendment which reads:
U.S. Constitution wrote:
Amendment IV (1791)
The right of the people to be secure in their persons, houses, papers and effects against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
However, note that "person" here means the actual physical searching of a person, and not simply observation or monitoring. As far as I can judge, the issue of public security cameras is up to the people of that community, and while truly invasive monitoring of every nook and cranny would likely be a problem, it is also a problem that would probably be best dealt with by local discussion and referendum.
Now the issue of security devices in airports and other public facilities (or facilities which serve a public purpose) that provide a (nearly) naked representation of the subject is another matter altogether.
Also, regarding the "granting homes in which to be private" idea, twisted liberal interpretations of the "General Welfare" phrase in the preamble aside, neither is there an enshrined right to receive largesse out of the public treasury (= entitlements).