I subscribe to several print periodicals, but none is a newspaper--all magazines (New Yorker, Nature, Astronomy, Nature Reviews Neuroscience, and I'd probably do a couple more if my wife agreed not to murder me). I still only read the newspaper online, but I have to say that I so much prefer the print editions. There's an irreplicable quality to flipping pages while drinking coffee in the morning. I don't see it as digital vs. print however. I think that they can exist side by side and add to one another. Print works for long articles, and things that aren't super temporal in nature, whereas digital is far better for keeping up on day to day goings on. I like both, but I will say that print never gives me a headache. Edit: It's sort of ironic that this is an article about the virtues of print whose headline is written in accordance with the traditional click bait internet style guide.
I've always said that the best way to keep up with the daily news is with a weekly magazine or newspaper. Important, complex stories require time and perspective to write about. Whatever doesn't make the cut by the end of the week probably wasn't worth reading about in the first place.
Yeah, that's my general approach too sorta. Although I just don't have a place in my life for long-form other than when I'm at work, and print stuff is harder to hide :)