I live just off Cape and we snowmobile in Rangeley, and someday I may have to see that area in the summertime! It's a 5 hour drive from here, so for me personally I'd do the entire trip in one day and not worry about the overnight stay somewhere.
That said, you can't go through Boston (propane tanks) so you'll have to take Rt128 (Rt 95), or 495 though that is at least 30 mins longer. Once you get north of say Exit 50 it should be smooth sailing up 95 into Maine and eventually Route 4 all the way into Rangeley.
Not sure what your GPS will try and do, but I recommend going through the Farmington area (route 4) and NOT come up the left side of the lake via Route 108 and Route 142.
While the views are beautiful that way, and it may even be 10 mins shorter, the road itself is a frost heave nightmare
Edit: I much prefer the WAZE GPS app over Google for smart phone navigation. It leverages Google maps but has the benefit of real time feedback from other Waze users, so things like construction or road hazards or a hiding State Trooper are updated in real time.
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