What prompts me to bring it up is this article over on GameSpot, which discusses rumours that Fallout 4 will be set in Boston:
If a new rumor proves accurate, Bethesda's next Fallout game will be set in Boston. A Reddit user going by "fallout4boston" claims the unannounced Fallout 4 will be set in the Massachusetts capital city.
This tipster says Bethesda has been "scoping out and researching" the city, and suggests the developer has a "strong connection" to the Massachusetts Institute of Technology, a prestigious research university near Boston. The Reddit user "may or may not be an MIT employee," according to the post.
According to the Fallout Wikia page, "The Commonwealth" was referenced in 2008's Fallout 3. Four real-world states in the US categorize themselves as Commonwealths: Pennsylvania, Kentucky, Virginia, and Massachusetts. Bethesda lead designer Emil Pagliarulo told 1UP in 2009 that the Commonwealth reference in Fallout 3 was in fact speaking about Massachusetts, not any of the other three states.
Additionally, Fallout 3 and Fallout: New Vegas included mentions of a mysterious "Institute," which is located in The Commonwealth. This could potentially be related to the Massachusetts Institute of Technology referenced by the Reddit user.
At the very least, it seems like a good guess. It fits with fleeting references in previous games that could obviously be expanded upon, keeping it on the east coast helps with it being a direct sequel to Fallout 3 and it maintains some separation from the west coast games of Fallout 1, 2 and New Vegas (though they're obviously still in the same canon), assuming they don't want to retcon a few things from Fallout 3 that differed a little from the first two games.
Having spent hours upon hours with Fallout 3 and Fallout: New Vegas, I'm definitely keen for the series to continue and am looking forward to a new game being announced soon. My guess is that even if they do disregard a few things from the west coast games and further establish a few different ideas about the Fallout universe in games set on the east coast, they'll take a few ideas and innovations that Obsidian made use of in New Vegas, such as better storyline branching, the companion well, signature weapon attacks and so on. It'll also presumably use the same tech as Skyrim.
If the Boston rumours are completely wide of the mark, then I'd suggest Chicago as a possibility. They've used it before but not in any of the fully canonical games, it's been established there's an Enclave base there which would work out well given their role as antagonists in Fallout 3. It's not east coast obviously, but instead sits fairly comfortably between the east coast and west coast settings, so it could feasibly borrow from both. If they do want to keep it on the east coast, New York seems like a good setting as well.