score:4
You should make sure that your baggage is checked through and can remain in the airport overnight, other than that and the fact that you'll be wondering around Newark and NYC in the middle of the night - I see no issues.
It will take you about half an hour to get to the city with a taxi, back would probably be better to take a train because of the mid-day traffic. I suggest maybe get an hotel to sleep for the night close to the airport and then take a train to the city in the morning.
Upvote:1
It doesn't sound like you need to worry about visa issues.
You will need to retrieve your luggage after you arrive in EWR. You may prefer to store some of it in the airport, rather than take it to NYC. Luggage Hero is OK - EWR may have other choices for that.
If you want to spend some of your 17 hours sleeping comfortably, you may want to rent a hotel room either in New Jersey (cheaper) or in Manhattan (more fun). I might just forgo sleep in your situation, but more likely I'd book a nice hotel in Manhattan, take a taxi there from EWR around 2-3am, rest a few hours, then hang out in Manhattan (make a list of things to see and do in advance), then head back to EWR in the afternoon - maybe as early as 2-3pm to beat the afternoon rush hour traffic, retrieve and check in the luggage, go through TSA security (sometimes that's an hour+ wait).
Mass transit (Airtrain + NJ transit to/from EWR; subway around Manhattan) is cheaper than a taxi, and more predictable. Taxi get stuck in traffic.