What are some good mainstream unbiased sources
Is the Syrian Human Rights Observatory a reliable source?
It's not (reliable).
The sad truth is that there is no single reliable source for the conflict. If you want to know what is going on there you have to follow a number of sources and go through a lot of propaganda to draw the median lines, if possible, about what happened.
EDIT 1: Explanation of the justification for the first claim
According to the Wikipedia article, this organization consists of one man, a former regime-dependent dissident who lives in Coventry:
The organization is headed by Rami Abdulrahman (sometimes referred to as Rami Abdul Rahman) from his Coventry home. He is a Syrian Sunni Muslim who owns a clothing store. Native to Osama Suleiman, he took a pseudonym during his years of activism in Syria and has used it publicly ever since. 
This should be a warning sign. As for its track record and impartiality:
SOHR was accused of selective reporting. AsiaNews said that for the first two years of its existence it only covered violent acts by government forces against the opposition.  SOHR has also been accused of reporting anti-government militants among civilians killed  and has been described as "oppositional"     or anti-Assadic.   It has been criticized for refusing to share its data or methods. 
Or in the words of a Reddit user that matches my experience:
It's decent. It's a pro-rebel site so it is pretty accurate when it comes to reporting wins and news from the opposition, but even then mistakes are common and sometimes the site makes claims that are ultimately completely wrong. There are worse sources out there (SyrPer or Malcolmite come to mind) but there are better sources too. I would avoid taking SOHR's word for granted when you see them making a claim or reporting a win / loss.
Besides, it's just a guy who lives in England. Idk how he gets his sources but it's not a group - it's a single person.
The thing is, I could find you cases where he clearly reported something wrong, but you could say that for any source in this war. For example, reporting dead militants among dead civilians, increasing the military casualties on one side and emptying the civilian casualties on the other and vice versa - these are all common and honest mistakes in conflicts that anyone who means well and agrees with limited resources, could make.
Patterns only emerge after you've followed a source for a while. They notice that one side never loses villages, conquers them again and again: P or that children only die from bombs in their controlled area or ...
It's not just SOHR, try following a source for a while and you will find that most of their local or twitter sources and possibly their allegiances seem to fall into broad categories: pro-government, pro-Kurd , Pro Isis, Pro-Rebel.
So my suggestion is to follow the situation closely with a number of conflicting sources and see for yourself. In this conflict, almost no one is going to give you real information that everyone agrees is the truth.
Open question is of course whether my suggestion to you, a mere SE user, to follow a number of sources and this seems to be the source not only for many journalists but also for the US government and UN bodies can this be?
The answer is probably politics: P journalists will usually (with a few rare and honorable exceptions) pick up a partisan source and then fucking retweet, SOHR for the uprising, Yusha Yuseef for the regime, Syrian Rebellion Obs for Rojava Kurds, etc.
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