In a city with so many great walking options and parks, I'd have to say that Greenwood Cemetery is one of my favorites. It's larger than you might expect, so every visit is a unique experience. Fortunately my favorite part of the now Historical National Landmark is very easy to find, as it's the main gate. A Gothic spired entrance, the gate is home to huge nests of birds, including wild parrots (!) though I've never seen one myself. On a crisp autumn day, it's great to watch the birds flying in and out and you can hear their cries from a long way off.
A nice way to continue for a walk is towards the huge, impressive chapel, then down to the Water Side Path that takes you along the Valley Water pond and fountain. If you continue down that path to Lake Ave,?make a left onto the windy Eglantine Path that offers plenty of large shading trees and a pretty view of Sylvan Water lake.
It's also a welcome place (they even hand out maps to visitors at the main gate) where many beautiful, strange, eerie, headstones, are around every bend and gorgeous foliage, trees, vistas and hillsides are there for you to explore. This visit we saw the grave of stained glass artist Louis Comfort Tiffany (other famous people buried here include Leonard Bernstein and Boss Tweed). On another visit we reached the highest point in Brooklyn where a civil war monument looks out at the Statue of Liberty in salute.
It's really a beautiful place to take a stroll and also a favorite of ours because its so easy to get to.