The biggest question for me is how to track important world or national events without tracking the 24 hour news cycle. I'd like to understand trends that unfold over weeks, but not days, like a low-pass filter on the news. The best I can come up with is reading the economist, but I'm looking for better ideas.
My news sources: NYT, BBC, CBC, The Globe and Mail, Toronto Star. I'm Canadian, as you might be able to tell.
Sometimes I read what Brookings puts out, but it's important to keep in mind their biases as a think tank.