What non-US paper though? In my experience as an Australian all of our papers are totally fucked. We don't have anything anywhere near as good as NYT or WaPo.
Crinkling News [1] was a surprisingly good Australian newspaper. It ceased publication in January 2018, but I gather they would reopen if they could find the money (Costs $200k/year to run?).
It was written for children, essentially the print equivalent of ABC's Behind The News bulletin [2]. The writing level wasn't too far removed from the "adult" papers (I gather broadsheets are written to a 12 year old reading level and tabloids lower than that). Articles were a mix of mainstream news and kid specific stuff. There were fewer articles than an adult paper, but was basically all there with the extraneous stuff removed. It was completely independent.
The Saturday Paper is quite good. It's only a weekly, but really, there's usually only enough truly important stories around to fill a paper a week, which is why there's so much ephemera and filler in the daily news.
It was written for children, essentially the print equivalent of ABC's Behind The News bulletin [2]. The writing level wasn't too far removed from the "adult" papers (I gather broadsheets are written to a 12 year old reading level and tabloids lower than that). Articles were a mix of mainstream news and kid specific stuff. There were fewer articles than an adult paper, but was basically all there with the extraneous stuff removed. It was completely independent.
[1] https://www.crinklingnews.com.au/
[2] http://www.abc.net.au/btn/