The Time Out magazine you can get at most kiosks is pretty decent, but its only updated twice a year, I think.
There is no weekly mag in english that tells whats going on.
You gotta do that online- paper is so last century, ya know.
http://www.timeout.com/buenos-aires/
http://whatsupbuenosaires.com/wuba2/
If you hit some of the stuff listed in the Agenda section of whats up, you will find interesting local music, art, and performance, usually with no tourists present.
and english- thats a bit of a problem- you see, they speak Castellano here.
depends on what you are looking for- there are lots of threads on this site about finding music, or tango, or film, or art.
Besides the two above, I like to hit these sites, for Art and music happenings.
http://www.ramona.org.ar/
http://www.buenosaliens.com/
What, in particular, are you interested in?
There are lots of websites for specific interests.