There are newspapers and then there are periodicals. Some of them are dailies, others are considered weeklies, and then there are those which are only published monthly. But less frequent is questionable and most of them should update their content online.
The Saguache Crescent is one of the oldest US small town newspapers that City Island Images could find that publishes the old fashioned way, but also regularly updates their news and information content for the online community. Publisher Dean Combs tells www.cimages.me the newspaper has been publishing since 1882 by his grandparents.
He publishes every Thursday and says he's never missed a day's work for over 35 years.
He points out that if a publication does not publish at least once a week, it's not considered a newspaper, but just a periodical and points out that many are publish information that is incorrect, out of date, or both.
Take a look at these links and see if you find your local small town newspaper and then look to see if you can find what their latest updated issue online.