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I used to live in northern New England and have stated more than once on these forums that it is next to impossible to find a road there that isn't scenic. The trick, especially in the fall, is to find one that isn't clogged with "leaf-peepers". Timing will help, if you can do most of your driving during the week rather than on weekends. But knowing where the 'back roads' are and sticking to them will be the key.
For instance: the main roads between Boston and Ottawa would be I-83/I-89 in the U.S. and then QB-133 and Autoroutes 35/10/30/15 through Montréal to the Trans-Canada and ON-417 to Ottawa. Those are all pretty much Interstates/Autoroutes/Motorways and not the best for enjoying New England. Then there are the heavily traveled 'surface routes' such as NH-16 and VT-100 that run north through the White and Green Mountains of New Hampshire and Vermont respectively. Those can be fine, but since they are only two-lane roads they can get clogged up, especially on weekends. The trick is to find little-used roads that go more-or-less in the direction you want and take you through cute towns and offer the occasional vista, historic site, or other attraction.
But first: After your trans-Atlantic flight, get a good night's sleep somewhere around Logan Airport. Money saving tip: most hotels near major airports will pick you up for free. Don't rent the car on arrival at the airport. that's expensive and you pay for a day you really don't need but get a good night's sleep first and then rent from an off-airport rental location with no extra 'tourist' fees. You can usually drop such a rental off at the airport on your return for no extra charge.
Some of my personal favorites can be strung together to make a scenic drive on little-used (albeit slower) roads: Take US-1 out of the Logan Airport area to I-95 north into Maine and take the Wells Exit to ME-109/ME-11/ME-5/ME-113 north through Sanford, Cornish and Fryeburg and Evans Notch to Gilead ME. From there head west on US-2 through the Shelburne Birches and along the northern edge of the White Mountains to Jefferson NH and NH-116 to Littleton. Next up, US-302 through Barre (Hope Cemetery is as close to a 'must-see' as there is in this area) to Montpelier and US-2, not I-89, to Burlington VT. Take the ferry over to Port Kent NY and US-9 north along the Lake Champlain shore to Plattsburg. Then it's NY-190/US-11/NY-122/NY-37 west (although US-11 will be marked 'south') to Rooseveltown NY where you'd cross the border into Cornwall, ON, Canada and finally ON-138/ON-417 into Ottawa.
The above route from Boston to Ottawa is obviously chosen for scenery and to take you through small towns, all the while avoiding traffic as much as possible. There are several worthwhile sites to visit, especially in northern Vermont in Barre, Montpelier, Stow and Burlington. But before we get further down into the weeds it would help to know whether such slower, less-traveled routes appeal to you and whether you want that level of detail in your route descriptions. From your post, I think so, and that you'll have the time for it. For a little more on what I might suggest, have a look at this Trip Report on our RoadTrip from Boston to Nova Scotia last year.
AZBuck