For mainstream news online, I've been leaning towards the New York Times lately, they're pretty good at factual reporting on a variety of issues, including some very interesting longer-form articles in the New York Times Magazine, such as
this one published Wednesday on the secretive financial system of places such as the Cook Islands and St. Kitts and Nevis. Which, while as financially exotic as it sounds, does have a fair impact on the rest of the world as well.
For more industry-specific news, I often visit Ars Technica and AnandTech, and while there are a lot of good articles there, it does not cover everything worthwhile. Ars Technica also has a libertarian slant, and while I'm sympathetic to that, it causes you to think that issues such as the Trans-Pacific Partnership aren't as nuanced as you realize they are when reading more comprehensive, non-commentary articles on sites such as the Times. Or put another way, it sometimes has issues distinguishing between reporting and commentary, as Sascha77 alluded to. What I consider the mainstream media in the U.S., IMO (and counter to Sascha77) is better at this distinction - although I suspect I'm thinking more of newspapers and their websites as mainstream; if sources such as Fox, MSNBC, and CNN are what you think of when you think of mainstream media, they may well be as bad or worse at that distinction.
I don't use news aggregators much these days, but when I do, I use Hacker News. It's tech focused, and some of the popular articles will only be interested to those who have a technical background (and sometimes a specific type of technical background), but you do get a variety of articles on a various of topics as well, and typically high-quality articles or reports. One day there could be an interesting article on clean-energy power plants in Iowa that's popular, the next day an archaeological discovery in the Caucuses.
In print media, I subscribe to the local newspaper on Sundays, which exposes to a wider variety of articles than I typically encounter online and thus helps broaden my perspective. It also is helpful for keeping up on local happenings, beyond my bubble in the city. The local paper does have a conservative bias (it's endorsed the Republican presidential contest in 24 of the past 25 elections, for example, the only exception being endorsing Clinton this year), but that's largely confined to the editorial and opinion section - again, doing pretty well at distinguishing reporting and commentary. One area in which it's superior to the Times is that I can get a variety simply by paging through the front section (Nation and World), whereas the most popular articles tend to raise to the most prominent placement on the Times' website - meaning, for example, that its website has been heavily focused on Trump since the election, while in my local paper I've received close to as much variety as I would in a typical month.
I also subscribe to The Atlantic, where I find the largest value to be its long-form journalism on a variety of topics, ranging from incarceration and drug policy to Chinese politics. Tonight I read two articles from the latest issue, one an interview with Henry Kissinger focused on his current thoughts on American foreign policy (conducted prior to the election), and the other an in-depth article on gambling addiction, its impact and prevalence, and the factors that (subtly) promote it within the industry. It's fascinating because the long-form journalism teaches you far more about a topic than you typically can (or are likely to) find online, while often covering more recent developments than you're likely to find in a book.
I've heard good things about The Economist as mentioned by Smellincoffee, too. I could see myself adding it to my list if I decreased the frequency of reading some of the online sources (there are only so many hours in a day, which is the same reason I only get the newspaper on Sunday).
Not recurring, but I also read books, although not usually on contemporary issues. Currently reading
1776 by David McCullough.
I don't watch TV news as I don't have broadcast or cable TV, and don't recall anything ongoing from when I did have it that I'd consider as high of quality as what I can get in print or online. Back 10-15 years ago Anderson Cooper had some interesting on-site reporting segments, but CNN moved more towards either towards partisan host-centric shows (e.g. Glenn Beck) or debates between highly partisan sides since then, as well as towards repeating the same five news stories over and over, so I don't consider them worthwhile anymore. Every so often there's an interesting documentary on PBS, but those typically are available later on DVD if I really wanted to view them. But in short, the amount of time spent viewing low-quality stuff to get to what's left of the high-quality stuff in TV news means it's not worth it.
Perfection beat me to my joke response, but on note of that, I don't use social media to discover news (or for much else, for that matter). The mix of news I could get from Facebook or Twitter is no more informative, in-depth, or broad than what I can get from mainstream (print-focused) sources, and all too often veers towards lots of people reposting whatever the pet topic du jour on Facebook is. Occasionally a friend mentions what that topic is at dinner, and I'm almost always glad I hadn't heard about it before when that happens as it's usually something inconsequential. Social media can be a good way to stay in contact with people, but I haven't found it to be good at keeping informed about the world at large.