I will have to try this weekly approach.
To start with, the NYT has traditionally been considered high-quality but since the internet age is torn by interests in attention-grabbing topics, controversial and contrarian takes, having SOMETHING to say about everything, and "being fair to both sides" (and to various class backgrounds) to maintain its "centrist" / "paper of record" industry position. Sometimes the long-form articles are high-quality, but often they are the way they are for some of those other reasons.
Every publication is going to have SOME bias, but as a starting point the Atlantic (leans left) and the Economist (pretty much defines Sober Neoliberal Center) are good. I like Harper's but it's more literary/essay-focused. A nice mix of substacks can be good. Most good writers will be annoying to you in some way, you have to put up with that for good informed writing, as opposed to "comfort zone" writing that is going to validate everything you feel by oversimplifying reality. E.g. I like Matt Yglesias' and Noah Smith's substack as news and as statements of a certain centrist/economic-realist takes, and good zoomed-out commentary on politics, but I find their contrarian voices on twitter annoying (:
In all the work is: finding writers you like, and resisting the urge to fall into things that are too comfortable or appeal to your "baser" tendencies, for informedness, to know what-to-think-to-be-on-the-right-side, etc.
Would also like to throw in the Wall Street Journal for news. If you stay away from the opinion sections, they are pretty firmly center and provide some great coverage of current events.
Incidentally, several of these (Atlantic, Economist, WSJ) are available on Apple News+ if you already happen to be paying for it.