I have a digital subscription to WaPo and I've found it interesting reading even as a European. But it's still clearly a local newspaper to a certain extent: some of the political reporting is ultra-specific to the point where it's barely understandable if you're not immersed in the Washington scene.

NYT is more generic, but also has a higher volume of articles about everything under the sun. For learning about the American situation, I've found WaPo a good compromise.

I'd also recommend WSJ for a generally balanced business-centric outlook on America (their editorial and op-ed pages are basically "more tax cuts!" regardless of what is going on, but the reporting is good).