Two Days (Plus) at a Relaxed Pace
It is, of course, possible to get from approximately Meadville PA (80 miles north of Pittsburgh) to Bar Harbor ME (outside Acadia National Park) while minimizing Interstates in general and toll roads in particular. It would take about two days of steady driving, plus whatever time you'd like to spend at attractions along the way, so certainly with three days, you could do it in a very relaxed manner. Basically, you'd take PA-77 to US-6 across northern Pennsylvania to just west of Towanda and then use US-220 up to NY-17/I-86 across southern New York to Binghamton. A short jog north on I-81 would put you on I-88 north, one of the most scenic Interstates in the east, and one that passes Cooperstown on its way to the Albany area. Getting through Albany requires a short toll segment on I-90 (the New York State Thruway), but then I-87 north is free to NY-7 east. Once past Troy on NY-7, your trip on back roads through New England starts. NY-7 takes you past Bennington Battlefield and then becomes VT-9. On the eastern side of Vermont a short drive north on US-5 along the Connecticut River will let you hook up with NH-9 which merges with US-202 which will take you into Concord and then continue on into Maine. At Gorham ME, leave US-202 and take ME-25 down into Portland. Explore the waterfront and the Eastern Promenade and then leave town on I-295 past Freeport to US-1 at Brunswick. US-1 will take you Down East along the Maine Coast to Ellsworth from which ME-3 will make the final jaunt to Bar Harbor.
As I say, that's a good two days of solid driving at a minimum. If you plan to stop at some of the places en route you should plan on a third day. There are many more possibilities for interesting stops than I've listed, but further recommendations would depend on how much time you have and what your interests are, as would suggestions for places to stop for the night(s).
AZBuck