Newspapers should shift gears and run more human interest pieces. Highlight the things going on in their communities that aren’t summed up in 140 characters, or an alert sent to the phone. Throw in some comics, the days weather, and sports league standings. They are very obsolete otherwise. Anything major read at 6am happened by 10pm the night before and isn’t news to anyone with a tv, tablet, or smartphone.
I think they are more valuable than just human interest stuff. It's the investigative journalism, especially at the local levels, that will really be missed. Think of all the stories of major wrongdoing that newspapers broke open over the years, often after many months of investigating and chasing down sources. CNN or FOX News definitely aren't going to do the legwork on that type of stuff.
Look at what happened at Northwestern as an example. Pat Fitzgerald was going to get two weeks off in July after a whitewashed Friday news dump press release. Then the student paper dug into it and interviewed a couple whistleblowers, and next thing you know the university changed its mind and fired Fitzgerald. No new information for the decision makers, just some of the details were public knowledge now. The cynic in me thinks universities everywhere are looking at that thinking they should severely cut funding to their student papers.