Although the noises of the city have their own charm, sometimes it's nice to find some peace and quiet. That's easier said then done in NYC, but there are a few spots in Central Park in which you might momentarily forget that you're in the most populous city in the U.S.
The dirt paths in The Ramble offer an opportunity to stroll through the woods with few other people around. In fact, I've never seen more than two other people on these paths.
Shakespeare Garden is another peaceful place to explore. It's generally a bit more crowded than The Ramble but still provides a fairly quiet retreat. I love the stone paths and wooden fences.