I thought that I would take advantage of the 50 state plus DC membership.

Does anyone have any recommendations for a small Mayberry type Americana town to hang out in from either -

Maine
Vermont
New Hampshire
Connecticut
Rhode Island

thanks for any suggestions.
Probably more like some time in September.

Your mileage may vary with any of these depending on what you are looking for and what you mean by "Mayberry type Americana town." The suggestions below range from VERY small towns (Rangeley, Maine has about 1000 year-round residents) to small cities (Burlington VT).

Maine:
Ogunquit
Rangeley

Vermont:
Burlington
Brattleboro
White River Jct (adjacent to Hanover NH)

NH:
Hanover
Woodstock
Sanbornville

CT:
Mystic
Darien
Storrs

RI:
Newport
Narragansett

You didn't include MA, but these are also worth considering:
Amherst
Stockbridge
Salem
Reading
Foxboro
Concord
Plymouth
Bourne
Sandwich

Thank you sir. I had looked at Burlington and read a little about Rangley.
I have a feeling it will be Rangley.
I hope someone there among 1000 can cook for a dairy intolerant.

Thanks Contrarian. My next step is AAA.
I left off Massachusetts because a trip to Boston is on my agenda.

I lived in St. Johnsbury, VT for a summer. Might be what you looking for!

Great choices by Contrarian. I would add to his list --

Bennington, VT
Woodstock, VT
Warren, VT
Hancock, NH
Great Barrington, MA
Chatham, MA
Kent, CT
Kennebunkport, ME

Some of these towns are right next to towns he listed (e.g., Kennebunkport & Ogonquit, ME)