When framed in terms of bias, the implication is that things in the centre are unbiased, or that the bias somehow equals out — that you get the best picture by reading those news sources.
...when the truth is that no news source is unbiased. Period.
Even if a particular source somehow manages to perfectly balance between whatever the current "left" and "right" are in that political environment, that doesn't make it free of bias. Sometimes the people on one side of the political spectrum in a given environment are genuinely, collectively, doing bad things! Sometimes there are personal biases! Sometimes the political environment shifts, and leaves you behind!
In general, it's much more important and productive to be aware of and transparent about your own biases than it is to try to present yourself as "unbiased".
You say that the WSJ is "more balanced and less biased than NYT", based on that website.
But a bias towards centrist American politics doesn't mean a lack of bias — far from it.
For example, 30 years ago a "centrist" report on global warming might have given equal space to right-wing and liberal perspectives, even though the vast majority of scientists at the time sided with liberals on the facts.
20-ish years ago a centrist report on Iraq would have parroted the administration's lies about WMDs and the urgency of going to war. And the New York Times was one of those organisations!
In any European country the New York Times opinion pages would be seen as pretty centrist, or even centre-right.
That so much of US media and political sphere skews heavily to the right distorts the overall picture.