I'd like to know if there are some maps giving the geographical coverage of the media publication, for example, a map giving the counties or even the cities where local newspapers are sold, and a map showing the coverage of the US radios?
Newspaper Map shows the newspapers for cities around the World, and even breaks them out by language:
For over-the-air media (like radio stations), it will take some data processing on your part, but you can find all of the data they collect for radio at the FCC Wireless Telecommunications Bureau (WTB) GIS page.
From here you can download geographic data for all sorts of over-the-air media-related information (see FCC licensing database extracts and FCC licensing market boundaries as well as some generic US basemap layers.
This data is undoubtedly the source for the NPR map referenced in another answer.
For radios : http://secure.nprlabs.org/maps/ (zoom on USA towns)
Here is another example from nprlabs (2007) :
"The NPR Labs Mapping And Population System provides terrain-sensitive coverage maps for reception of all public radio and television stations in the U.S. The maps are designed to guide station- planning efforts to improve reception and develop new services, including new FM and TV stations and translators, as well as HD radio and mobile TV."
For local newspapers coverage : I'm sorry, i'm not sure this kind of map exists