If I start sounding like a Tory, you'll know why. I've started getting most of my news from reading The Economist.
"Conservative" is a relative thing. The Economist is a specifically European form of conservatism, one where the Texas death penalty gets special attention, Barack Obama has already won the nomination, and industry abuses in California are called out.
I particularly appreciate the international viewpoint. So much better coverage of world affairs than American news outlets. I feel like I understand something about what's going on in Kenya, Zimbabwe, Japan, Brazil, and more generally internationally. And the outsider view of US politics is interesting too, from election coverage to a sort of direct assessment of American wiretapping politics. It also helps that it's a weekly magazine rather than a daily, the stories are a bit more thoughtful.
I read the New York Times for years. It's an excellent paper but after the Iraq war runup disaster I lost faith in their editorial board. The recently bungled McCain story doesn't help anything. I still read the local paper, but it's become a joke. I'm finding I don't quite finish one copy of The Economist before the next shows up, and that's just about enough weekly news for me.