Personally, I only cross NYC at night....like 3AM night. The trucks start to roll at 4 A.M.
Too much commercial traffic during the day as well as business commuters who live on L.I. and work in NJ. Avoid rush hours completely and the times in-between will be pure luck. One accident can cause congestion that will keep you in traffic for 2,3,4,5 hours. Make sure you have a full tank of gas when you enter NYC, you never know how long its going to be.
IMO, you have 2 options.
1. take the Tappan Zee Bridge across the Hudson River rt 287 then south on rt 95 to Long Island.
2. if you have a jam up , this is the more expensive option but can be a good option. Take the Tappan Zee Bridge then head north on rt 95 into Conn. you'll have 2 optional ferries to cross L.I.Sound and land in Suffolk county near riverhead NY.
https://www.longislandferry.com/Common/Help.aspx?page=fares One is in Bridgeport Conn to Port Jefferson NY (25 mi. west of riverhead) . The other is n New London Conn and lands in Orient Point (30 mi. east of Riverhead ). Its a nice ride and offers a relaxing cruise for an hour or so. Pets are welcome.
I would keep the phone number handy just in case, make a reservation while your on the road, it saves you an RV spot on board the ship.
I did use the following route some years ago .
I would avoid the G. Washington bridge rt 80 into rt 95 Cross Bronx Expy.
It's too congested and on separate trips , I broke one WH hitch and one aluminum frame rail on the trailer. A lot of potholes.
I would head east on rt 80 thru PA and pick up rt 287 to cross the Tappan Zee bridge.
Con't down across rt 287 to rt 95 south. This will give you 2 options to get onto long island in the queens area (actually NYC)
1. The Whitestone Bridge , cont down the Whitestone Expy rt 678 to rt 495 (long island expy)
OR you can take the Throgs Neck Bridge rt 295.
I prefer the Throgs Neck Bridge to the southbound Clearview Expy rt 295 , then take rt 495 east to wherever you need to go....Riverhead is the east end of rt 495 exit 72.