Yeah, that's the way. And you're right, you'll want to obey speed limits in the NH towns; Dublin is one that has a low limit about which they're fairly serious.
For a more relaxing drive overall, though longer, use the Taconic Parkway out of NYC Metro, then run across Vermont via NY 22 and NY 7/VT 9. Or as a compromise, use Taconic-MassPike-91 to Brattleboro. This lets you avoid traffic in CT, which may be desirable in terms of both congestion and behavior.
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