I think the description at United States/Tags – Places is pretty good for northern New England:
place=city
Cities at the center of metropolitan areas, always incorporated, with a metropolitan population above 50,000 (a rather small city — most cities have much larger populations — up to many millions of people). Some boomburbs are also tagged as cities, given their size (>100,000) and continuing growth.place=town
Smaller-sized towns or cities (which may or may not be incorporated), including suburbs (as that word is known in US English to mean “smaller incorporated city near a different, large center city”), generally with a population between 10,000 and 50,000 within incorporation limits. In sparsely populated rural areas, cities with a population less than 10,000 are also tagged place=town if they are state capitals (capital=4 — rare, though Montpelier, Vermont qualifies), county seats (capital=6) or otherwise especially important centers of civic activity with more-major amenities such as hospitals, universities, courts, dozens of commercial and/or industrial businesses, etc. Some place=town POIs represent population centers within unincorporated areas. These POIs may lie within census-designated places (CDPs) but do not necessarily correspond to them.place=village
Small cities and villages with a population generally less than 10,000. In sparsely populated rural areas place=village will have fewer amenities than place=town with only a bare minimum of commercial and civic amenities. (A consensus is emerging that a “village” has at least a small commercial landuse area: a market, a fuel station/convenience store, a bank, et cetera, this is flexible as of 2023) Some place=village POIs represent population centers within unincorporated areas, such as former villages that have disbanded.place=hamlet
For isolated settlements with fewer than about 200 residents.
As an example, Burlington, Vermont has a population of 44k, but is the central-municipality of a 108k-person urban area, so would just barely make a cut for place=city. In contrast, Rutland, VT is the second-largest municipality outside of the Burlington urban area at only 16k population and may not make the cut for place=city. I’d be fine with Burlington being the only place=city in Vermont.
It’s likely that different guidance would be needed for southern New England where the higher population gives suburban neighborhoods larger populations than stand-alone Vermont towns.