The Ground Zero mosque
(Atheist writer Sam Harris has an overview of the broader issues here; try to put the "Islam is a peaceful religion misinterpreted by extremists" clichés on hold long enough to read it with an open mind.)
In any case, mosque opponents are not wrong about Islam being evil; what they are wrong about is the proper way to respond to evil. We've been through this kind of issue before with groups like the American Nazi party, NAMBLA, Fred Phelps, etc. However repulsive their ideas, the proper solution is not to prohibit the expression of those ideas, but to refute and attack them with free expression of one's own. That's how conflicts in our society should play out; that's what the First Amendment was intended to provide for.
Rather than trying to stop the mosque from being built, how about trying some of that "free expression of one's own"? One possibility would be a museum or center in the same area, dedicated to Islamic crimes against humanity and their firm roots in Islamic sacred texts and theology, encouraging people to get the truth for themselves. There are ex-Muslims such as Ibn Warraq and Ayaan Hirsi Ali who could serve as consultants on such a project (the biggest challenge would be to prevent it from being co-opted by some other cause like the political right or Christianity). Based on the level of opposition the mosque has aroused, financial support wouldn't be a problem. For that matter, on balance the mosque itself is probably already a public-relations loser for Islam, and a vote-winner for Republicans (especially given some liberals' knee-jerk denunciation of opponents as bigots) -- which is their real reason for raising a fuss about the issue, of course.