As a Brit I would say BBC news has declined massively in quality over the last 20 years, and has become strongly biased - not towards either side of politics, but rather, towards being excessively positive to whatever government is currently in power (both Labour and the Tories have benefited). This isn't even a product of them being state-funded, because they're not, really, and the government has little control over them, but rather due to more subtle and complex factors, and the pressures of the 24-hour news cycle.
However, for international news, they're still usually pretty good unless that issue interacts with Britain/the British government. For example, they're pretty bad on Israel/Palestine these days, because if they don't take a firmly pro-Israeli government stance the get pilloried in the rest of the press and by the government as anti-Semitic*. Even 10-15 years ago their reporting from the region was superb, perhaps the best of anyone, and even daring and made people care. It's a real pity.
Weirdly the Financial Times has extremely good reporting, but is heavily paywalled. When I feel like subscribing to a British news source, that'll usually be the one. It's actually less mindlessly pro-capitalist, significantly so, than almost any other UK paper, which is just bizarre but there we are (stark contrast with the absolute lunatics at the Wall Street Journal - I can demonstrate their utter lunacy in a single info-gram they once produced if anyone disputes it).
The AP aren't bad but have a distinctly biased style guide which significantly damages the quality of their actual reporting, especially on gender issues.
Entertainment news, like others I tend to go with Variety and The Hollywood Reporter.
I weirdly enjoy reading the LA Times. I presume it's biased in some way, but it's a fascinating and somewhat insular paper.
Won't touch the NYT with a bargepole unless it's a scoop or I'm bored in a waiting room - their scoops are often amazing, but their day-to-day reporting is of highly questionable quality and their opinion columns absolutely wild yet utterly predictable. I still remember a very lengthy Ross Douthat opinion column which was about "immigrant estates" in London, a thing that literally doesn't exist. It was clear what had happened. Ross had been "picking up [cigarette butts]" as we say (I don't know if the filter will let me use the actual term, even though it's not obscene here) - i.e. half-understanding other people's conversations. And he'd constructed this entire fantasy world in his head, and was using his column to moan about it. He was vaguely simultaneously trying to imply the English were racist (true, but not in the way he was making up), and the English were right to be racist. Bizarre stuff and extremely representative of the quality of NYT columns - I do recommend NYT Pitchbot on Twitter, who makes up sadly plausible NYT headlines:
Gaming/geek news I generally only bother with Kotaku and io9 (Gizmodo), and reddit boards, because virtually every other gaming site has gone down the content farm/corporate tubes (Eurogamer and RPS less so, but they're both very boring these days). Sadly G/O Media would like Kotaku/io9 to go the same way.
* = To be clear, no-one actually believes that, outside of a lunatic fringe, but the British press are obsessed with point-scoring off each other, and will do that in preference to actual reporting. It's like a horrible insular private school - exactly the kind of school most of the owners and senior editors (and columnists) went to (and I did, for full disclosure).