There are herds of wild deer a half hour outside NYC. Deer seem to be able to thrive anywhere as long as there aren't many predators.

The continental US (i.e. excluding alaska) has some 20+ mil wild deer, 200k bison, 1 mil bears, 3-4 mil coyotes, 13,000 wolves, 5 mil alligators, 10k+ mountain lions, etc, etc. Yes, most are in the vast western states. But deer and bears are common even in areas a just a couple hour drive outside of NYC. Thankfully no gators near NYC (except in the sewers, of course :-)