Some links and places to start for outdoor bouldering and rock climbing in New York City etc.

Polish Traverse Harriman State Park some boulders there Worthless Boulder, Central Park NYC Ape Boulder, Bennet's Pond

Central Park is good:

Fort Tryon / The Cloisters, Van Cortlandt Park at the Northern end of Manhattan and into the Bronx

Harriman State Park:

The Ice Pond, located near Brewster, NY

Bennet's Pond (Ridgefield) located near Danbury, CT: