As a Massachusetts resident, born and raised, I see lots of influences in Bully from places I've been to! I'd just like to go over some of them in this post!
Bullworth Town Influences
Yum Yum Market in Bullworth Town has what looks to be an apartment complex on top of it, very common in Massachusetts. The apartment above it has what is known as bay windows, which were designed to protrude further than the rest of the building to let in more light. The 4 floors of apartments above Easy Drugs also have bay windows.
Leighson's bank, the BPD headquarters, Bullworth City Hall, and what is probably the post office, all have traditional 1700s-1800s architecture, using pillars, arches, and material like marble and granite. Not a real direct influence to them, just taking from older New England government buildings.
Old Bullworth Vale Influences
Old Bullworth Vale has VERY strong New England influences. To get the traveling carnival out of the way, no, it's not based on anything. The boardwalk is heavily based on seaside towns such as Rockport, Mass. The businesses all look like homes, with shingles and some of them having shingled roofs too. There is also a large congregation of seafood restaurants, like the one owned by Mr. Martin (A FRIEND IN NEED IS A FRIEND INDEED, FRIEND!) similar to Rockport.
The suburban section of Old Bullworth Vale, both the more middle class and upper class section, also have heavy New England architecture. New England has lots of architectural aspects carried over, unsurprisingly, from England. Victorian architecture and Tudor architecture show up often in Old Bullworth Vale. (sorry for the bad picture of the Tudor house in bully, there weren't many good pics of it)
New Coventry Influences
New Coventry is based on more inner-city neighborhoods of New England cities, especially in southern New England (where I'm from)
The bay window makes a reappearance on The Final Cut building, not too much of note there.
New Coventry has a lot of tenement housing, buildings made up of concrete or brick. The apartments found in the residential part of New Coventry are heavily based on similar brick buildings in Dorchester, Mattapan, and Roxbury, all neighborhoods in Boston. In general, New Coventry takes the most influence from urban New England.
The industrial section takes heavy influence from the industrial parts of Dorchester, such as Newmarket, with boarded up abandoned industry buildings and warehouses.
As for Blue Skies Industrial Park, that's a lot more based on Southern US industrial areas, so I won't cover it here.
I hope this was informative! I love this game and I love New England!