Many cities have weekly publications across the nation who claim to be part of the genre "alternative newspaper." There are in fact very few true alternative newspapers in any given city, USA.
This said because many of these publications are part of a chain of news agencies, owned by big conglomerate corporations.
Their layouts and departments, such as news, arts, music, movies and classifieds, are all pretty much the same, which belies the term "alternative."
Much closer to the mark would be independently owned weekly newspapers, such as the "Austin Chronicle." But this publication still follows a set format. It publishes no alternative stuff, such as poetry, graffiti art, or outrageous prose penned by local anarchists.
The most "alternative" publication I have ever encountered was the "Berkeley Barb," which had its heyday from 1965 to 1980 in the Bay Area of California.
Unfortunately, it has gone the way of the dial telephone and manual typewriters.
Read more about it here: http://en.wikipedia.org/wiki/Berkeley_Barb