CNN posts plenty of information about people opposed to vaccine, without mentioning conspiracy theories. They have posted plenty of direct statements from such people. They also have unbiased reports and direct quotes about HCQ. You can learn as much about HCQ and the controversy from CNN as from any other mainstream medium that I know of.
People often confuse left vs right bias, with factual content.
All media will take a political line left/right/middle, and use this to alter the balance of their reporting. You have to make value judgments when describing things. One person's left (or right) will be another person's "middle of the road" unbiassed.
Here is a great visual representation. The point is you want near the top, and it does not matter whether left/right/middle. It is true that politics away from the middle tends also to be mixed with less reliable reporting but in principle that need not be so.
CNN is not too bad, but not great. CNN web a lot better than CNN TV. Fox TV News is quite a lot worse, Fox web news better than TV. Personally I don't like TV as way to get news - it tends to have less info and more emotive content (images and music). I listen to BBC R4 news in preference to BBC 24 hours TV news. That is also why I don't much like the YouTube stuff posted here. If you want the facts instead of the PR go for written reports.
If you want to be well informed the key thing is the factual content. Is there lots of it? Are the claims made well supported, or completely unsupported. And if you want political information (e.g. what is a fair judgement of Trump's effectiveness as OPUS) you should be reading well informed stuff from the centre, or from both left and right. Personally I can't stand Trump's character and style. In terms of action, I can see how someone with a more right-wing philosophy might like much of what he does. I also note that the "old-style" Republicans see him as dangerous and unsuited in character in the same way I do.
The conspiracy theory stuff, whether left or right wing, is not factually supported. Otherwise, given its sensationalist content, it would be headline news everywhere - not conspiracy theories!