You're right, the NYT isn't perfect; far from it. They don't know many things they should, and they sometimes fall prey to their own biases. But they're still a lot better than MSNBC or Yahoo (I'm not sure how they can be compared to Fox News, which "reports" more fiction than fact, so it can't really be considered news at all). You can't really go to Yahoo and see what's going on. At best you'll get anecdotes collected by the news agencies, but they don't have the people to put it in context.
Fox News during the day[1] isn't terrible other than their love of the same "hot" story but their is really no difference between them and CNN these days. MSNBC is 100% pundits all the time to the embarrassment of NBC's actual news staff. If you mean the IRS or Benghazi as false stories then we would have a bit of a disagreement given the documents the gov has released and that whole e-mail story.
Yahoo is an aggregator for normal news and does have quite a bit of original content in selected verticals. I will say they point to local papers that tend to get it right. I don't see any advantage to the "putting it in context" when it is such a prejudice and not-very-well-facted-check lens. The NYT (like CNN) is riding on an old reputation.
CNN asked if a black hole could be responsible for a missing airline flight.
1) at night is a whole different story - everyone has pundits everywhere
