Yes, mosques should have the freedom to set up where they want. This the right of Americans, not allowing a mosque to be placed in certain area is discrimination based on religion. All Muslims are not terrorist and all terrorist are no Muslims so it would be asinine to ban a certain place of worship from setting up in a particular area.
The ideology that led to the the terrorist attacks of 9/11 was based directly on the intolerant, violent, and hateful nature of Islam.
Islam preaches that non-Muslims (to whom Islam refers to derisively as 'kuffars') are inferior to Muslims. Further, it preaches that non-Muslims ought to be subjugated, or better still, wiped-out.
Given the highly violent nature of this belief system, it would be most unfair to allow the construction of a place of worship for the followers of such a system.
These acts of terror are called for in the Koran:
Quran (2:191-193) - "And kill them wherever you find them, and turn them out from where they have turned you out. And Al-Fitnah [disbelief] is worse than killing...
But if they desist, then lo! Allah is forgiving and merciful. And fight them until there is no more Fitnah [disbelief and worshipping of others along with Allah] and worship is for Allah alone. But if they cease, let there be no transgression except against Az-Zalimun (the polytheists, and wrong-doers, etc.)" The historical context of this passage is not defensive warfare, since Muhammad and his Muslims had just relocated to Medina and were not under attack by their Meccan adversaries. In fact, the verses urge offensive warfare, in that Muslims are to drive Meccans out of their own city (which they later did). The use of the word "persecution" by some Muslim translators is thus disingenuous (the actual Muslim words for persecution - "idtihad" - and oppression - a variation of "z-l-m" - do not appear in the verse). The actual Arabic comes from "fitna" which can mean disbelief, or the disorder that results from unbelief or temptation. Taken as a whole, the context makes clear that violence is being authorized until "religion is for Allah" - ie. Unbelievers desist in their unbelief.
Unlike nearly all of the Old Testament verses of violence, the verses of violence in the Quran are mostly open-ended, meaning that they are not restrained by the historical context of the surrounding text. They are part of the eternal, unchanging word of Allah, and just as relevant or subjective as anything else in the Quran.
The context of violent passages is more ambiguous than might be expected of a perfect book from a loving God, however this can work both ways. Most of today's Muslims exercise a personal choice to interpret their holy book's call to arms according to their own moral preconceptions about justifiable violence. Apologists cater to their preferences with tenuous arguments that gloss over historical fact and generally do not stand up to scrutiny. Still, it is important to note that the problem is not bad people, but bad ideology.
So, in conclusion, it would be a very bad idea to allow Muslims to build a triumphalist mosque on the grounds of 9/11.
Mosques should not be allowed in the vicinity of World Trade Center's ground zero because it is a slap in the face of those who died. There are so many other places a mosque can be built, it does not need to be built there. Even if the Muslims building the mosque do not support Bin Laden's thinking, they need to respect the fact that it is his view of Muslim thinking that brought about 9/11.