I don't know my way into NYC from that direction. I have only ever gotten into Manhattan by bike via ferry rides from Hoboken, Jersey City and, most recently, Staten Island. (Our local bike club does a yearly ride from New Hope, PA, to Brooklyn.) You'd have to get to the GW Bridge way up north in Manhattan to actually ride in. Personally, I would not want to be bothered with riding in the traffic-heavy areas of north Jersey.
The map I linked to picks up the ACA route "south" of Norfolk, CT. You have to go backwards a bit if you wan to reach Lone Oak Campground, which I believe is the only game in town until the Millerton, NY area, where there is the Rudd Pond section of Taconic State Park. (Closes after Labor Day.) Lone Oak used to offer have a cyclist discount. Relatively inexpensive compared to what a normal site costs. The place is a huge camping resort. To me, the in-ground hot tub was worth it.
I have done the ACA route south from Poughkeepsie through Port Jervis, etc., a few times. It's mostly nice, although I would skip the trail mileage starting in New Paltz and instead stay on the roads the route used to use. The segment south from Port Jervis through the NJ side of the Delaware Water Gap National Recreation Area is one of my favorite local-ish long weekend adventures. Worthington State Forest along that stretch is a great place to camp. (It often fills on the weekends during camping season. A weekday is the best time to go.) Saw a bear cub there in 2018. The 13 miles from Belvidere to P'Burg is wonderful. There are some low, narrow railroad underpasses that mean no truck traffic. In general, there is very little traffic. Getting through P'Burg sort of sucks, but once you get back down to the river at Carpentersville Rd. the riding gets really nice again until Milford. Dogwood Haven Campground, just across the river, gives a cyclist discount. Mark, the owner, is a great guy. Small, "rustic" and quiet, with nearly all seasonal people who are pleasant, although when I was there last September I there was a couple riding the ACA route north.