Welcome to the Big Apple! Consider yourself luck - New York City is somewhat of a mecca for enthusiastic runners. Not only is it home to the New York City Marathon, one of the world's most popular marathons held each year in early November, but it is home to dozens of running clubs and groups with miles and miles and miles of road to cover. And with Central Park being a prime location for runners, trail running in New York City is fantastic too! Fortunately for you, Central Park is closed to cars (as of this summer) so you can take to the park's roads without fear for your safety.
There are many loops to choose from, depending on how far and difficult you want your run to be. (For instance, a full loop through Central Park is not quite a 10k, at 6.1 miles. Running this loop will take you through some of the Park's highlights. But this loop can easily be shortened or lengthened too - you can choose to loop back sooner so as to run less or double up loops to run more.) Aside from the main loop, you can choose to run the Reservoir Loop (around 1.5 miles) which offers incredible views of the city's skyline, or take the (literal) more off beaten, unpaved paths on one of the two Bridle Path Loops (the shorter loop is 1.66 miels while the longer loop is 2.5 miles).
Basically, no matter how little or how much you want to run, you can manipulate your route so that you can accomplish your running goals. Start out by getting a map of Central Park's running loops and roads, and study it to tentatively map out where you want to run. You can also get involved with an experienced running group who have lived in the area for a while and are familiar with the trails. Or, maybe even better yet, you can join in on one of the Park's running tours. Two tours, Fit Tours NYC and City Running Tours, offer group running classes in Central Park. Especially since you are new to the city, this could be a great way to both learn which trails are your favorite and meet new friends (and potential running buddies!).