A great primary source, often non-web/electronic, will be a town's own newspaper. Most of these will be available on microfilm at the city's
public library. They often have some sort of vertical file of local events, which may be things beyond newspaper clippings. If they are, you will be able to get citations to actual articles. Some towns' newspapers may or may not be indexed, but because you are dealing with a particular time period, it shouldn't be too bad.
Check the public libraries' websites to see ahead of time how far back the town's newspapers go back. Most towns have a local history collection too, and you might find more material in those.
Think of things like the Board of Health reports, Mayors’ reports, City Council minutes.
Even if you are not working on Boston itself you may want to pay a visit to the Boston Public Library, especially the McKim Building (on Dartmouth St, Copley Square). They often have information on other cities and towns besides Boston. They also have a large collection of Massachusetts town newspapers on microfilm. Don’t forget to make good use of the reference librarians – that’s what they are there for. You can also achieve electronic access from home to some sources. All you need is a local library card. That can be to BPL or a closer library like Medford or Somerville. You can also get a card – or rather ecard– online for BPL http://www.bpl.org/general/circulation/ecards.htm. All this is free.