Some center-right outlets that are still worth reading* (and I say this as a raging leftist):
The Hill, National Review, Foreign Affairs, Wall Street Journal, The Economist
*(as in they provide both informational "what's happening" and insightful analysis without venturing into flat out fake news... as long as you avoid their editorials and comments)
I suppose those are "classically conservative" news outlets, as in "small government but with a general respect for evidence-based governance, science, and the truth". I don't know of any reputable populist-right/alt-right outlets. I don't know if there even IS a reputable populist-right/alt-right movement to begin with, but that's another discussion.
Side note: Google News (as of a year or two ago, when they revamped their algorithms) unfortunately now also gives you a bunch of worthless blogs and fake news (the literal kind) outlets. I have hundreds of sources in my "never show this source" blacklist and even then it's barely usable. That said, it's still a useful way to see different takes on the same topic. Their grouping algorithm is a lot better than their vetting algorithm. Some of those sources should just not show up for anyone.