A thought. The Guardian feels like a local paper to me, much in the same way as The Tenby Observer did when I was growing up. This could be because I spend some time moored a few meters away from their office. But in contradiction to this The New York Times also feels like a local paper to me, even though it's based the other side of the Atlantic, in a city I've never even visited. What make the NYT feel local to me though is pretty much based on having watched these two films recently I think.
Both films allowed me to form an emotional connection to the paper, that I otherwise wouldn't have. Especially being able to put people behind the otherwise context less references to David Carr (a former drug addict turned straight talker), Brian Stelter (digital wonder kid) and Bill Cunningham (the oldest and most eccentric style blogger you'll find).
So local is obviously working on a few levels for me. Location and shared values, but also a relationship to the individuals connected to the thing in question. I don't know if this means anything in particular at the minute, but it might one day.