Cataratas Iguazú

The park on the Argentine side is called Cataratas Iguazú. There are paths on this side that take you along the top. There is also a walk way that takes you a little over a half-mile out in to the river--about half of its width at this point. The walk way brings you to within a few feet of the Garganta del Diablo.
Here you can get a close up look at what it would be like going over the edge. 
From a hundred feet away the Throat of the Devil doesn't look that menacing. The only thing that gives it away is the roar.
Another fifty paces reveals a different view.
See the video.