In my experience this is a terrible mistake. The answer to violent Islam is not Islam. And contra every liberal pundit practicing their religion of peace and acceptance speech, building a mosque by ground zero is not a counter-argument to violent Islam. It is an apology, and an offering, to it.
The answer to radical Islam is liberal, pluralistic, democracy. There’s a reason for that. Islam itself is screwed. No major Islamic leader in the world today preaches a message even remotely close to what most of the new American “let’s build the mosque” crew would find even barely tolerable.