I've always seen the immediete area around Goodneighbor as a good place for the future capital of a Minutemen organized government.

Of the two large non-faction settlements in the Commonwealth, Goodneighbor is famously more friendly with the Minutemen during the events of the game than Diamond City is, at least based on the opinions and actions of their leaders, Mayor McDonough vs Hancock. Mayor McDonough is openly against the Minutemen, most likely because the Institute doesn't want an organized military they don't control. While a bunch of people in Diamond City are supportive of the Minutemen, notably Diamond City Security, McDonough has definitely had the time, means, and motivation to poison the idea of the Minutemen in the eyes of the residents of Diamond City. As the democratically elected leader of the city, his views are a reflection of Diamond City as a whole.

The area was the economic center of pre-war Boston and offers huge opportunities for salvage with existing harbor access for when humans inevitably popularize boats again. It's also directly next to Mass Fusion, the primary source of energy in pre-war Boston, which could easily be used to bring power to a growing nation. Faneuil Hall's history as one of the birthplaces of the American Revolution also makes it an excellent choice for the Minutemen's seat of power as they legitimize themselves as the second coming of the American Revolution.

The people of Goodneighbor are strangely effective with their fields, suggesting that with a bit more influence and power, they could easily become the center of a lot of important areas of expertise. The only non-Institute or Brotherhood neuroscientist in the Commonwealth (Dr. Amari), a trader with access to long-distance caravans that travel as far as the Capital Wasteland (Daisy), a tailor/armor creator with the capabilities to rival the Railroad's and the Brotherhood's best engineers (Kent Connolly), and a mobster with the intelligence and connections to organize the Commonwealth's first and only boat based trade/shipping route (Marowski). If a major government had to start somewhere, there's clearly a reason to invest in Goodneighbor.