I'm skeptical about trying to find perfect neutrality. Getting reporting (and opinion) from several different POVs seems better to me. It's a fair amount of effort though.

Foreign papers are a good way to get a different perspective. Especially important when the topic is US foreign policy. I like British and Australian ones.

I wish I had a sane US conservative media outlet to recommend. Surely there is one? For the libertarian angle on current events, reason.com is a decent substitute. But that's mostly opinion, not news reporting.