York, Maine

York is beautiful, Durham is alright - but both just posh, slightly out of touch northern towns similar to Bath.

And if you want to rely on public transport, I’d look at places like Edinburgh, York, or Copenhagen. All easy to get around without a car, not usually crazy hot, and plenty to do with kids.

You could hit York on your way for one night

Somewhere like York and around Yorkshire would be fairly nice and there's some quaint little towns to explore (Harrogate, Beverley, Knaresborough, Ripon etc).

You’ve definitely got to go to York.

Arriving at 7:00 AM, I had the sunny streets all to myself—truly magical.

Fly into Boston and rent a car or take the Concord Coach or Amtrak up to Portland (or even Portsmouth, NH). York, Kennebunkport, Boothbay. Late summer is beautiful (Aug/Sept/early Oct), but April or May will likely be cloudy and/or rainy for the vibe you want. Lots of woods, small town diners and shops, fishing towns, and friendly locals to learn from.

If London isn’t your thing then 2 day/1 night trip to Bath, York, Liverpool or Edinburgh are often recommended.

I'd sooner recommend York, Bath, Liverpool, Manchester, the Peak District, Lake District, or Cornwall for places in England.