Agreeing with others to avoid Franconia Notch and instead use Rt 112 from the CT river over to Conway. Beautiful scenery the entire way.
But that's only if you really need to go to the Whites at all, as it's sort of out of the way and in truth, the SW portion of NH is as pretty and has better riding with fewer tourist traffic then the Conway/North Conway region. One option for Vt as well is to head south from Burlington on local roads, skipping Rt 7, then head east over the Greens at Rt103 south of Rutland, which is preferable to Rt 4. Or head south from Plattsburgh, cross the lake at Essex, NY to VT on the short ferry, then head south then east, thus avoiding Burlington altogether. Then south to Rutland and east to SW NH. Any road will do as long as it's a state numbered road as opposed to a US Numbered Hwy (2,4,5,7, etc...)
SB