I can't speak for every local but the "local paper" where I live is effectively the RSS feeds of the local CBS & NBC news stations' websites and the reporting is actually quite good, or at least, it's a LOT better than receiving no local reporting.
The actual local paper is as you describe. I don't understand why local TV has weathered the digital transition better, exactly, but I find that I get a LOT of the local coverage that I want this way and I'm eager to recommend this to strategy to others (as you can see)