Pretty much everyone goes around NYC and not through it. The usual route around is I-95 south to 87 west across the Tappanzee Bridge and then south on the Garden State Parkway. I would not call it scenic, but the views going over the bridge can be nice. In clear weather you can see NYC in the distance. Then as you pass the city you catch views here and there of it as you head south. The time of day is important. On weekends there is much less traffic, if you can manage it. During the week, avoid 7-10am and 3-8pm. The Merrit Parkway in CT is a nicer alternative to 95.
If you're not visiting any of the cities along the way such as Philly and Baltimore, I have a nice scenic route for you from NJ to DC. Take the Garden State Parkway to Cape May, NJ, then take the Cape May/Lewes Ferry to Lewes, DE. Then take 404, the Sea Shore Highway to rt 50 into DC. If you have a wait for the ferry, Cape May is a beautiful old fashioned seaside town, worth a drive through.
Thank you that sounds like a good option.
As mentioned, the route over the Tappan Zee is the alternative, I think it's 287. You would catch the Merritt Parkway, which is a pretty route, just after New Haven. Going through the city via the Bronx Expy is often just one long crawl, sometimes I actually have taken this route for that reason, the rest of the area is crazy fast, but good drivers, unlike in RI and MA.