Battery Park is the green wedge at the very bottom of Manhattan, where the island runs out and the harbor opens up. From 17 John Street it's about a 12 to 15 minute walk, straight down toward the water. You can head down Broadway past Bowling Green, or cut over to the waterfront and follow the promenade the whole way. It's one of the few spots in the Financial District where you can stand still, look at open water, and not have a skyscraper right on top of you.
It's also the launch point for the boats to the Statue of Liberty and Ellis Island, so a lot of people pass through on their way somewhere else. That's a shame, because the park itself is worth slowing down for. Here's how we'd spend time there, and what's worth knowing before you go.