What they don't tell you until you show up is that this isn't the actual dueling grounds site. Here's the verbiage of the plaque:
"Somewhere below this site, on a wooded ledge twenty feet above the Hudson River, lay the dueling grounds. Among the many known and unknown duelists who fought here were Governor of New Yor, DeWitt Clinton (1769-1828), Secretary of the Treasury, Alexander Hamilton (1755-1804), Vice-President Aaron Burr (1756-1836), and U.S. Navy Commodore Oliver Perry (1785-1819). All came ot Weehawken to defend their honor, according to the custom of the day."
The site itself is on a gorgeous path overlooking the water. Great area to do baby strolling or walking to burn off the calories in the morning. Tourists really don't come to visit here, so this is more of a curiousity for passerbyers than anything else.