As pulsar said, it would help to know what part of NC, plus, withing your parameters, not going to or even near NYC is doable, but to stay away from tolls, makes it harder, not going too far out of the way, is a matter of personal choice, like, how far out of the way, road condition is probably the hardest to nail down, while interstates are generally the widest straightest flattest, they can also be the most boring, and even they have places that are fairly rough.
NOW, were it me, (or I), I would run I95/295 south to I495, over to I90, then I84 thru Hartford, & Danbury, and Newburgh, NY all the way to Scranton,Pa. and pick up I81 south to at least the I64 Jct.in Va.. from there it would depend on what part of NC.
Now, you may consider this too far out of the way, plus it will not get you out of all the tolls.
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