Wikipedia: Rat Rock (Central Park)
Rat Rock, also known as Umpire Rock, is an outcrop of Manhattan schist which protrudes from the bedrock in Central Park, Manhattan, New York City. It is named after the rats that used to swarm there at night. It is located near the southwest corner of the park, south of the Heckscher Ballfields near the alignments of 62nd Street and Seventh Avenue. It measures 55 feet (17 m) wide and 15 feet (4.6 m) tall with different east, west, and north faces, each of which present differing climbing challenges. The rock has striations caused by glaciation.[3]
 
Boulderers congregate there, sometimes as many as fifty per day. Some are regulars such as Yukihiko Ikumori, a gardener from the West Village who is known as the spiritual godfather of the rock.
     
Central Park Conservancy
UMPIRE ROCK
LOCATION West Side at 63rd
Located in the southwest corner of the Park, Umpire Rock is named for its location in what was Central Park’s first playground, a large open meadow where children could play games such as baseball. The rock now forms the backdrop to Heckscher Playground and still provides views of Heckscher Ballfields, just to the north. The rock is a destination for climbing, exploring, and picnicking as well as enjoying views of the surrounding scenery, including the Midtown skyline.

Umpire Rock is also a place to explore the geology of the island of Manhattan. Central Park is home to innumerable rock outcrops, making it one of the few places in the City with visible evidence of the island’s ancient bedrock. Known as Manhattan schist, this bedrock was formed around 500 million years ago and contains other minerals, including quartz, mica, and feldspar.
 
Google Groups: rec.climbing
Rat Rock
Mkword
Apr 9, 1996, 3:00:00 AM
>>Looking for bouldering site, namely Rat Rock
>>in NYC. Would appreciate location of said
>>rock.
>>Dennis

Here’s the description from “A Climber’s Guide to Popular ManhattanBoulder Problems”—

“Rat Rock is located in Central Park at the 62nd Street level adjacent to the Heckscher Children’s Playground. Easiest access is from either Columbus Circle entrance or the Central Park West entrance at 62nd Street. Immediately north of the Heckscher playground and south of the Heckscher softball fields, walk to the north or east side of the large rock formation. Though officially labeled Umpire Rock by the City Parks & Recreation Dept., the climbers that come here have named it for its smaller and more permanent residents.”
 
Google Groups: rec.climbing
Rat Rock in Central Park, N.Y.
Ed Hartouni
Apr 29, 2003, 2:30:17 AM
I used to climb there in the late 70’s… I agree with Shilajit that the ‘Gunks are much better…
 
Tim Toula’s Rock ‘n Road gives the best description:
 
“Manhattan. In Central Park. Rat and Cat Rock on 63rd St. Rat at W side of park near baseball fields. Cat on E side of park near bridge and pond…” I don’t know if the baseball fields are still there.
 
Tim notes: “... Rat Rock has long traverse and is slightly more pleasant then fondling a dull razor…” which I recall is true. But desperation is a climber trapped in Manhattan unable to get to the ‘Gunks (note that you can’t repeat George Willig’s desperate “big wall” anymore). Back then we didn’t have climbing gym’s, there are several in Manhattan which are quite good.