Lived in the area for decades and worked in the South Bronx. It's all a **** shoot. My suggestion is GWB to 87N to 287E, take NY 22 N(exit 5, iirc) and get on 684 N in Armonk, NY, to 84E. Plan on fuel in NJ or 87N and then there is fuel just over the CT border on 84.
95 - the CrossBronxXpwy, and the New England Thruway are packed, especially Friday afternoon northbound, fugetaboutit!!!
I would camp north of Waterbury CT; the Bristol suggestion appears to be a good call. There is at least 1 campground on the CT River north of Hartford as well.
And whatever you do don't get on a Parkway.
