Honorable mention to John Mauldin's newsletter Thoughts from the Front Line -- not a "news site", per se, but it has a nice level of insight into economic matters for the non-technical (maybe semi-technical) reader.
I don't really read news (don't care much about politics and world events). Mostly specific subreddits about tech and my hobbies, blogs, hacker news.
From time to time (maybe once a week) I will read a newspaper website in my native language (a small local European news company which has been quite objective in my view) just to not be completely clueless about what's happening in the world.
You might like the free section of this closed-/open-source scienticific publications resource (labs can opt-in to open-source their research), called Thieme medical publications. Here's a link [1] to my favorite journal of theirs: Planta Medica. I wouldn't have imagined any kind of lab toiling away to get funding in plant pharmacology research--until I found planta medica.
2. Money Stuff by Matt Levine from Bloomberg View
Honorable mention to John Mauldin's newsletter Thoughts from the Front Line -- not a "news site", per se, but it has a nice level of insight into economic matters for the non-technical (maybe semi-technical) reader.