In fact, you are absolutely wrong about that. It's called the power of eminent domain, and a government can use that power to take someone's private property to use it for a public purpose.
You must be one of those "the U.S. Constitution is a living document" and can mean whatever the politicians and bureaucrats can get away with.
Article. I.
Section.8.
Clause 17: To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;
Actually, I'm one of those who thinks the Constitution means exactly what it says. The clause you quoted has absolutely nothing to do with this case or any other case involving a local government involved in an eminent domain proceeding. The clause you quoted deals specifically with the U.S. Congress -- it gives Congress the power to exercise authority over any lands that are purchased by the U.S. government (with the approval of the state legislature) for any of the various purposes you listed.
For a real application of Constitutional law to the case in point I'd recommend that you read the Tenth Amendment, along with this specific clause in the Fifth Amendment:
". . . nor shall private property be taken for public use, without just compensation."
In the Piscataway case, nobody is claiming that the municipality is taking the property without compensating the owner -- the issue is only whether the compensation is "just" or not.
To sum it up, folks: The Fifth Amendment of the U.S. Constitution clearly allows for the taking of private property for public use, provided the owner is adequately compensated.
Section 8 is titled "Powers of Congress." These enumerated powers for the our "federal government" have nothing to do with the powerso of state and local governments.