The Hill is surprisingly good for DC politics news.
The English version of Al Jazeera is Saudi-funded but usually covers stories fairly. (The arabic version is outright propaganda and should be avoided).
Vice News is pretty good. They have a new HBO show coming out.
The Intercept tends to get its facts right and sources them well. It's pro-Snowden and pro-Wikileaks but I haven't noticed any egregious slanting of the truth, or outright lies so far.
Even CNN (really!) has a couple of "real" journalists left working for them. The only one that seems to have enough clout to avoid editorial meddling is Fareed Zakaria (GPS).
John Oliver is biased, especially in terms of pro-Clinton content but his facts are usually correct. He's also funny.
Le Monde Diplomatique (French newspaper) used to be very good but I haven't read it in some time.
The BBC is generally accurate (and I give them props for funding an undercover investigation of their own director!) but I'd generally ignore it for hot-button UK-based political issues. It's one of the few sources that are legally-bound to be impartial however so they generally don't get TOO egregious.
The WSJ is still excellent for business news. Similarly the Financial Times in the UK. I'd largely ignore anything else they print however.
For the rest: I suggest just reading a story and then going straight to the source material to see how trustworthy it is. Any story that simply references another news outlet can be ignored - keep digging until you get to the actual sources then ask yourself if they are credible.