The First Amendment says that Congress shall make no law regarding the establishment of religion. Islam is protected by the First Amendment like any other religion. The Tenth Amendment gives the states (which are sovereign entities in their own right) jurisdiction over issues within their own borders. The City of New York (which is chartered by the State of New York) has an well-established permitting process for projects like "Park 51." The local community planning board has permitted this project, under the authority granted to it by the State and City of New York, and the federal government has no power to overturn that decision.
The lot at 51 Park Row (which was a Burlington Coat Factory store pre-9/11) is private property, and the owners of that lot have determined that this is the best use for that lot.
There are many on both the left and right who say the "Ground Zero Mosque" should be built somewhere else--- but there probably is no Somewhere Else. Even there is a Somewhere Else, it will be very expensive to start over at another site. Even though construction hasn't started, the project has still incurred all sorts of expenses: a site plan has already been drawn up, a permitting process has already been gone through, etc., etc.
This isn't Second Life: the owners can't just buy land on another sim and re-rezz their prims. This is real life. The owners of 51 Park Row may not even own a suitable property elsewhere in the city. It certainly would be non-trivial to buy an equivalent lot farther from the World Trade Center. And even if the owners do have other properties to choose from, they still have the right to pick the property which best suits the needs of this project. They even have the right to build their Islamic center near the World Trade Center. 9/11 doesn't just belong to non-Muslims: many Muslims were killed that day alongside Christian, Jews, members of other religion, and even non-believers.