Whether the community you're researching has or doesn't have a newspaper will depend on different variables.
A simple Google search that uses terms such as the name of the town, the name of the state and local newspaper will probably yield links to one or more newspaper websites.
Here are two examples:
To find other online news for a city, try using Google News Search with your own keywords.
You can also look at Wikipedia's List of U.S. Newspapers by State and Territory to find (incomplete) lists of published, defunct, and foreign language newspapers. Once you have the title of a publication, try searching for it online or contact local libraries to see if they have archived digital copies.