If you go thru Jersey and go over the GW bridge - that'll put you on the Hutch for about 5 seconds then to I-95 and take you thru connecticut onward to new england - while i don't understand why you'd want to - you are actually bypassing new york city proper and are skirting the city briefly and just staying on highways.
Or you can pick up 287 in New Jersey (nortwest part of the state) and take that over the Tappan Zee bridge ( a very cool bridge - even better if it's not a very sunny day - there's usually sun glare traffic) from the tappan zee you can hop on the Merrit Parkway and take that thru connecticut - the merritt is actually a pretty highway and last i checked - there were no trucks allowed on it.
If you're brave and feel like venturing a little - you can head out to the north shore of long island - or is it south shore - i'm bad at geography - head to orient point (have lunch with Sportswidow) then take the ferry over to New London Connecticut - if you're lucky you'll get on the ferry boat that's named after me
The drive out to orient point is beautiful - lots of windy roads and you pass at least one winery... It's a nice area of long island
or even to block island, ri (but then you'd have to ferry back...