Well I don’t live in NJ/NY so I’d map it out.
https://maps.app.goo.gl/vr7jaMhtuywupgAP8?g_st=i

Funnyish story though, this no bikes thing has happened to me thrice on my bicycle adventures.

• In Norfolk, VA I went straight instead of making a right and promptly landed on 64, with no way to go backwards, I hopped a fence and landed in an industrial park with a decent coffee shop, remapped my route and then gave it another go.
• In trying to flee hurricane Irene on a particularly long road trip, I ended up having to cross the St John’s river bridge because the ferries by that time of night were closed and I had to get into Newport News to stay at my friend’s for the night. It was a shitty situation all around. I feel it was the closest to death I have ever been in my life and I have had a few doozies. I do not recommend ever ever doing this and will never do it again, ever.
• Recently from El Escorial to Madrid with limited cell service, I landed myself on M-503 for a stretch. While this kind of road with broad shoulders in the US permits bikes, they do not in Spain. I was able to pull off onto a finca road and then eventually a greenway, but not before crossing a beautiful large rust colored bridge (with a decent shoulder).

I’ve been long distance biking for 20 years now and have had some excellent adventures, so fortunately these kind of wrong turn experiences have been few and far between.

There is a really great documentary on PBS right now about a group of kids who crossed the entire US on bike for charity in the early 80s, I highly recommend it. https://www.pbs.org/video/once-in-a-lifetime-qtroq8/