AJE - AlJazeera English is good for world news and objective US coverage - but not very in depth on the US side (which is why I like it). BBC is OK as well. I also like GPB news.
Unfortunately, Charlie, I also find most news (?) sources biased one way or the other. It's good to find a real right wing site and a left wing site - compare them on a single issue and split the difference to get an approximation of the truth,
Too much work for most people.
Charlie I am kind of like Bryant; I like fox for general (non-political) news because they seem to cover things others don't but if it is political I always double check CNN for a second view.
I have Google chrome and google news is pretty good because they use news sources from everywhere!Reuters, AP, Washington Post, WSJ, AJC, NYT just to name a few and many,many international papers-I like the variety -it appeals to my ADD and like Bryant I find that I can't find ANY news source that I totally agree with, so I check them all out and make my own decisions about the truth.
NPR has a nice website, Reuters and the Associated Press show up on a lot of the aggregators like the aforementioned Google. You're certainly right to look to a variety of sources rather than just one, a trick the Internet was--literally--invented for. I'm not a big fan of paywalls, which you run in to on sites like the NY Times and LA Times (they allow a certain number of "free" views per month.
Also, for longer-form, in-depth journalism, I love the magazine websites of publications like The New Yorker, Atlantic, The Nation and others. A pretty good cross-section of right and left is available and long-form tends not to be as abrasive or dogmatic, even when coming from a certain political point of view.