The 21-acre park is named for the cannons built to defend residents after the American Revolution. Castle Clinton National Monument (the place to purchase tickets for the Statue of Liberty and Ellis Island ferry) was built, as a fort before the War of 1812, though it was never used as such. You'll most likely recognize Battery Park for the prominent role it played in "Desperately Seeking Susan", Madonna's first movie. Besides the requisite T-shirt vendors and hot-dog carts, you'll find several statues and memorials scattered throughout the park. This is quite the civilized park, with lots of STAY OFF THE GRASS! signs and Wall Streeters eating deli sandwiches on the many park benches. Pull up your own bench for a good view out across the harbor.
Battery Park is probably the most interesting in aspect of all the parks in the city as it is probably from Battery Park that you get the best sense that you are on an Island. From Battery Park you get spectacular views of New Jersey, Staten Island, and the Statue of Liberty. If you fancy yourself as a bit of a New Yorker and you like life to whiz passed you, then Battery Park is one of the best places to roller blade in the city. It has long straight flat stretches for the beginner and plenty of obstacles (mostly in the way of pedestrians) for the more advanced bladers. However, if you only go to Battery Park for one reason, you should go to see the Trade Center memorial. The globe that sat in between the two towers now rests in Battery Park.