EVERY news source is biased, one way or another. And most of them are pretty bad.
I find it refreshing to read the international feeds for a little different perspective.
Look on the lower left of Drudge to find a long list
http://www.drudgereport.com/I like Wall St. Journal (they charge for EVERYTHING and much of their news feed is liberal, but some is okay. Their editorials & articles are better. You can read their headlines for free, and just google for more info if a topic interests you : ) & Fox (tho they have lots of stuff I definitely don't like!)
Their news often has a liberal bias, but their editorials are often better.
MUST read on Fox: Todd Starnes on Fox.
Euronews & Reuters both have some good stuff sometimes.
BBC World has the occasional good article, but their liberal bias in general news is downright nauseating.
I use "Feedspot" to read blogs, and for news I can simply put in a topic and it will supply my an assortment of news on my topic. For instance, you could enter "Mozambique" or "Hong Kong" or "Gun control" and they'll bring you an assortment every day on your topic : )
To me the best methods are:
Surf to a wide variety of sources.
Don't let any one have your 100% readership - cross reference & check them out!
Avoid TV news like it was Crack. Which it generally is
Hope that helps.
And, if it's like nails on a chalkboard - take a break for a few days. If the world blows up in that time SOMEONE will let you know ; )