I think it is not so much that there are places that are always accurate, or not susceptible to their own institutional biases or blinders. I think the trick is to try and remain aware of how the particular news source has approached certain issues over time, and to remain critical of a particular report or analysis if it happens to fit the narrative of that particular source.
That said, my own personal list of sources that are generally down the middle or just a little off keel would include the Christian Science Monitor, the International Business Times, the Skimm, Reason, Politico, Real Clear Politics (and its associated sites), the WSJ news pages, and the Hill (although it seem to be drifting right lately). In addition, there are certain sources, particularly on line sources, where the reporting on particular topics is generally insightful, even if the source is pretty openly ideological. Slate used to be at or near the top of this list although it is sliding more and more into the fever swamp lately. Instapundit is still a great aggregator of news. On foreign affairs, I really like a guy writing at the Belgravia Dispatch.