Title says it all, though here's what I count as the actual functional NY Metro Area. Passaic County Bergen County Essex County Union County Hudson County Middlesex County Nassau County Queens County Kings County Richmond County Bronx County New York County Rockland County Westchester County Fairfield County
Somerset, Hunterdon, and Monmouth Counties in NJ are all within an hour of Manhattan. So is Sussex in NY. Sure you don't want those?
Bronx Zoo Central Park Zoo Queens Zoo Prospect Park Zoo Staten Island Zoo New York Aquarium Bergen County Zoo Turtle Back Zoo Cold Spring Harbor Fish Hatchery & Aquarium Long Island Game Farm Long Island Aquarium White Post Farms Never been to any of them, but from what I've seen they all fit a definition of a zoo in some way or another. Edit: I have no idea what counties their in, but I would start by looking at those.
I’d count the following as well: Trevor Zoo Trailside Zoo Beardsley Zoo Norwalk Aquarium Space Farms Great Adventure Safari
Great Adventure Safari is an oft-overlooked jewel because it's not a zoo. They participate in SSPs and have a very impressive collection of megafauna and endangered species. They must have 20 scimitar-horned oryx! But they are in Ocean County, one county further than Monmouth. If you include Somerset, you get Duke's Farm, a large horticultural preserve that has a licensed program for managing wild bald eagle breeding. Duke Farms | Eagle Cam And Space Farms is in Sussex.