It is impossible for nonbiased news. My newspapers are The New York Times and Wall Street Journal, sometimes I read the Washington Post for pressing presidential or Congressional news as an addition to the Times. The Times is what every public official reads. It has enormous imptce. The Times has a definite liberal stance but it is not unrestrained liberalism. It is the newspaper of record. Obama reads the NY Times, as did Bush and Reagan.
My TV sources are CNN and PBS. Charlie Rose on PBS is utterly fascinating. I also watch C-Span regularly. They cover public stuff as a service. Washington Week is also good.
For international news and perspective, The Economist is priceless. It is very expensive. Foreign Affairs is crucial if that is your interest.
Vanity Fair and the New Yorker are also good sources for me.
This is the Eastern media. I find them very fair and balance. Yet I always strive to remember their mind set is the same as mine. To balance this fact, I may read National Review, the Wall St. Journal. I will not degrade myself by reading Fox News. Their commentators are idiots who know better. George Will is a decent conservative source. David Brooks is ok, too. I try to expose myself to conservative and libertarian thinkers who have the same great quality as the New York Times, et al but have a different bias.
I adore the NY Times. As a teenager, I walked up tall hills for quite a distance to purchase a copy. Educated NYers adore the Times (but we supplement it with the Daily News or Post if something major is happening in the city.) . Everyone in DC reads The Times. A friend joked that New Yorkers don't have a thought or opinion in their heads until the Times tells them what to think. This is very true.