New York City may surprise you-there are hidden trails everywhere, including the famed cross-country loop in Van Courtland Park. If you ever want to test yourself against some seriously fast people but don't have a running group, just head here and wait around-someone will be there to pass you by shortly.
For tamer running in city limits, check out Inwood Hills or Alley Pond Park for technical, meandering trails that make you forget the city is even there.
In the summer, there's very little that's more enjoyable than running on the beach (and then hitting the trails). That's why Sandy Hook is the best trail run destination when the weather is good (though it's pretty great in the winter when it's deserted as well). It's a bit harder to get to than some city parks, but well worth the trip.