The foliage turns from north to south, and from inland to the coast. At any particular point the transition from moderate to peak to post-peak is only about two weeks, so a week can make a difference.
The State of New Hampshire has a foliage tracker which will give you a pretty good idea, at least for New Hampshire, what areas are going to have the most color when. You can check out last year’s progression by moving the slider. Pretty much every year is going to be similar in timing.
https://www.visitnh.gov/seasonal-trips/fall/foliage-tracker
Because the progression is basically north and west to south and east, I would NOT go up the coast first. Better to head up Western New England into the interior and then head east to Maine and then down the coast, you’ll be following the color.
The White Mountains of New Hampshire will be at their peak right around Columbus Day, and it should be good a week either side of that. Central Vermont is probably about the same. Also the Connecticut River valley in Massachusetts is beautiful, but I don’t know when it hits peak, not that it has to be at the peak everywhere. You could easily find out.
Coming up from New York I would come up through Connecticut taking Rt. 84 to Hartford, then head up 91 north, into Massachusetts, and continue up the Connecticut River valley. Once you leave Massachusetts the Connecticut River is the border between Vermont and NH, running up the Vermont side. You could take 91, visiting Vt. towns along the way, and can easily cross over into NH pretty much anywhere, although there are only a few major east-west roads. I would consider picking up US Route 302 in Vt. and then heading east which will take you over to Franconia. Franconia Notch is one of the highlights of the White Mountains. From there you can take Rte. 93 south through the notch until Lincoln, then take the Kancamagus highway, Rte. 112, east to Conway. The Kancamagus is a scenic highway through 4000 foot mountains. Alternatively you can stay on 302 and come down through Crawford Notch, also ending up in Conway. At this point you’re just a few miles west of Maine. You can continue on Rte 302 into Maine, generally southeast to Portland, and then follow smaller coast roads down through New Hamphsire’s 13-mile coastline into the North Shore of Massachusetts. Gloucester and Salem have plenty of history. There’s also a little-known place called Hammond Castle in Magnolia that’s worth a visit. It has a view of the Reef of Norman’s Woe, from the Longfellow poem the “Wreck of the Hesperus.”
From the North Shore of Mass you can take Rte. 128/I-95, bypassing Boston, to the Massachusetts turnpike west to Sturbridge, where there’s a recreated 18th century NE village, akin to Williamsburg, which I went to twice as a kid and enjoyed it. At Sturbridge you can take 84 back through Connecticut to the NYC area and continue south.
Book early, and good luck.
Castle in the Clouds in Moultonborough, NH has good views of fall foliage and overlooks the north shore of Lake Winnipesaukee.
Thanks for all the suggestions!!