A: That's a terrific question. Newspaper editors understood that their papers would be read beyond their immediate town. Editors want to get the news out beyond their town to inform and extend their reach and increase their subscriber base. They routinely carried news from the wide surrounding area and beyond.
Tip: Search all of GenealogyBank for the specific surname you are looking for and limit it by the distinctive name of the town where they lived, like "Gilmanton".
Let's see what we have for families from Gilmanton, NH. I did an initial search and found more than 8,000 "hits" ranging from articles in the old newspapers to recent deaths in the town. I picked one article/family at random just to see what I could find on this family.
Here is an example of a typical "probate" legal announcement with a Gilmanton connection. (Published, NH Sun 21 Dec 1805). It concerns the minor (under age fourteen) sons of the late William Swain: Perkins and Gorham Swain. It states that they have land in Gilmanton (likely their father's farm) and that their guardian Thomas Balch recommended that the land be sold and the money put at interest for the care of the two boys.
A quick search of GenealogyBank showed more articles about Gorham Swain and Perkins Swain. Here is the wedding announcement of Gorham Swain and Sophronia N. Ranlett. (Published 26 March 1825. Portsmouth (NH) Journal of Literature & Politics). Notice that in this article his surname is spelled Swaine.
And here is the marriage of his brother Perkins Swain to Sally Weymouth. (Published 15 Jan 1823 - Portsmouth (NH) Journal of Literature & Politics.
The next article I found was the sad news that Sally (Weymouth) Swain had died on 14 Jun 1834 and that although he was in his "usual" good health at her funeral, he died a few days later on 24 June. The article ends with the words: "They were carried to the grave by the same bearers". (Published 25 July 1834 - Baltimore (MD) Patriot).
The Concord, NH newspaper the New Hampshire Patriot (21 July 1834) added that "Elder Knowles of Gilford preached at the funeral of each."
Newspapers around New Hampshire, Massachusetts, Vermont and even far away Maryland carried this poignant story.
Newspapers make it as real as today's news and give us the details we just won't find anywhere else.
Here is the advertisement for the auction for their farm on 2 November 1835. (Published New Hampshire Patriot 2 November 1835).
Bottom Line: Don't limit your search to only the "local" newspaper. Newspapers from around the state and country may have picked up the stories of your ancestor's lives. GenealogyBank is the best source of old newspapers on the planet. Period!