In the past I was able to access the New York Times through one of my memberships, which allowed access to ProQuest, but that benefit is no longer available. I am currently researching the libraries in my area to find out which ones might have a subscription to ProQuest or something similar that allows access to newspapers.
You mentioned that the New York Times site was free, but I was not aware of that. In the past, when I have found something from a Google search I have gotten a message that there is a fee to read further, or, that there is a fee for unlimited searches for a limited amount of time. Maybe things have changed since I last tried to search the Times. I will look into that.
If the newspapers have been filmed I can use the Family History Library, but in the case of the Record and the Herald News, it looks like I have to go to the source...or at least the town library.
Thank you for your wonderful suggestions. Things change so quickly on the Internet, it is important to remember to "look again".