I'd actually recommend the Economist - the writing is generally pretty good (in my opinion), but more importantly, as a weekly publication rather than daily, it's less knee-jerk about getting out the story quickly, and more focused on actually understanding the news and the implications of it.

I learn more from reading the 2 front page summaries (news + business) in the Economist than from all my internet daily news reading.

I also cut out mainstream news consumption.

For the most part, I simply haven't missed it. Events worthy of my attention (i.e. that will change my behavior) tend to bubble up through more specialized news sources (like Ars Technica or my Twitter feed) anyway.

That said, I have found NextDraft (http://nextdraft.com/) very useful.

http://www.stratfor.com and the like.

Protip: If you abandon your subscription in last stage of the cart and come back later, it knocks 50% off the price. It did for me anyway.

Last Week Tonight by John Oliver is a good source of news when it is in-season.

[1] https://www.youtube.com/user/LastWeekTonight

Sibling mentioned The Economist; I read Prospect for similar reasons (it's monthly, so even more so), and reading something a bit leftist helps balance something a bit rightist. (I also read TIME, but I hear the US edition is quite dumbed down, so maybe only if you can get a European or Asian edition).