Off Eastern Parkway near the Brooklyn Museum, you'll find a staircase that leads away from the bustle to the second-highest point in Brooklyn. (The highest is Battle Hill in Green-Wood Cemetery.) To call it a "mount" is generous—it's only 200 feet above sea level—but it served as a lookout point for the Continental Army during the Battle of Brooklyn in the Revolutionary War as they defended the Heights of Guan (now the neighborhood of Gowanus) from the British. There's not much of a view these days thanks to the buildings that have sprouted up around it, but there's now a playground and a wide lawn for lounging high(ish) above it all.

Not all of Prospect Park is equally maintained; one area that until recently had fallen particularly into neglect was the Rose Garden, which sadly hasn't had a rose growing in it since the 1960s. But in its heyday in the 1880s, the garden bloomed and boasted a pool with goldfish swimming inside. Earlier this summer in honor of the park's 150th anniversary, the the Connective Project to install 7,000 sunflower-yellow pinwheels in the onetime flower beds. Keep an eye on this spot: It's the focal point of the Prospect Park Alliance's new restoration project.

This extravagantly named chunk of parkland takes its title from a Thomas Moore poem about a region of Northern India. It was once a children's play area and then a formal garden, but much like the nearby Rose Garden, it's fallen into disrepair. Since then, the area has come to resemble a fairyland, with flowers and trees growing wild in an abandoned fountain. It's also held an important place in the history of Brooklyn's gay cruising scene, as documented in photographer Thomas Roma's book In the Vale of Cashmere. The Prospect Park Alliance is beginning restoration efforts in the Vale, removing invasive weeds (using goats!) before beginning reforestation in the area.

Deep in the center of the park, this lush woodland holds the title of Brooklyn's only forest. Olmsted and Vaux designed the Ravine with Adirondack landscapes in mind, and as such it's an oasis of winding trails, waterfalls, rustic bridges and even a small gorge. Erosion and overuse threatened the forest until reclamation efforts began in the 1990s, and now it's almost back to its former glory. If you're looking for wildlife in the park, this is the place to find it.

This carousel near Flatbush Avenue is a few notches above your average kid's ride. Built in 1912 by master carousel maker Charles Carmel, its elaborately decorated wooden menagerie includes 53 horses, a lion, a giraffe, two dragons, and a deer with inlaid with real antlers. The carousel was restored in 1987, and can be ridden today for $2 a pop.

This small area off the Upper Pool is notable not so much for its beauty but for the park visitors who frequent it: Brooklyn's endless, varied parade of dogs. Particularly during off-leash hours in the early morning and evenings, the shallows of Upper Pool are swarming with frolicking canines cooling off after a run in the Long Meadow. The beach reopened after renovations just this summer, having replaced its ugly concrete entryway with stone slabs meant to mimic an Adirondack streambed.

If Prospect Park's weirdest tree looks like it came from another time and place altogether, that's because it did. This knotty, twisting elm was donated to the park in 1872, using a cutting from the singular trees that grew on the estate of the Earl of Camperdown in Dundee, Scotland. The elm fell into neglect until it was saved from the ax and restored to health thanks to Pulitzer-winning poet Marianne Moore, who used it as a symbol to help found the Friends of Prospect Park. Moore even wrote a verse ode to the tree, in which she dubbed it Brooklyn's "crowning curio."

The park's extensive Lakeside project, which opened in 2013, included the restoration of several original Olmsted and Vaux landscape elements that had been bulldozed to make way for Wollman Rink in the 1960s. Among the revived areas is this shady grove facing out onto the lake, which originally served as a venue for live alfresco performance. Its musical legacy lives on in 19th-century busts of composers that dot the grove, including the likes of Beethoven, Mozart and Grieg. The grove also includes the dubiously named Oriental Pavilion, designed in the 1870s to approximate a Middle Eastern architectural style.

Though it's closed to the public, you can still catch glimpses inside this small, 19th-century cemetery on the southwest side of the park. Opened in 1849 by the Society of Friends, the graveyard actually predates the park and is now private land within it. Among the prominent Quakers buried here are Raymond Ingersoll, former Brooklyn Borough President, and Montgomery Clift, the midcentury Hollywood heartthrob who died young in 1966 and was buried here at the behest of his Quaker mother.

The best views to be had in Prospect Park are from atop this 177-foot-high hill overlooking the Lake. At the bottom you'll find a monument erected to the memory of the Maryland 400, a company of American troops who held the hill while Washington's army retreated during the Battle of Brooklyn in 1776. There used to be a wide path for well-to-do Brooklynites to take their carriages up the hill, but these days you can go on foot via a stone staircase. On a clear day when the leaves are off the trees, you can see all the way to Coney Island.

Also known as the Grecian Shelter, this neoclassical structure on the southern end of the park was designed in 1905 by legendary architect Stanford White. (He was murdered a year after its completion.) Open to the air and held up by limestone Corinthian columns, the Peristyle looks like it might have fallen through a time portal from Ancient Greece. It was added to the National Register of Historic Places in 1971.

Situated at the very bottom of the park across Parkside Avenue, the Parade Ground is a 40-acre expanse dedicated to sports of all stripes, with public spaces for baseball, football, tennis and soccer. In the 19th century, the Parade Ground was used for military drilling by the Union Army and the Coast Guard. Today, it's famous for a different reason: The ballfields here have been early swinging grounds for dozens of World Series-winning MLB players, including Sandy Koufax, Tommy Davis and Joe Torre.