It's perfectly grammatical, but a bit ambiguous. Your friend would need to know which way you were travelling to work out which side 'before' was. If you said 'the other side of the Post Office' then in context I think that's unambiguous: from where you were when you said it, it can only mean one side.
The problem with both phrases is not grammatic, but that both 'before' and 'other side' are relative, and without more information - which way you were coming from, where you were when you said it - the side meant cannot be inferred.
Also, 'before' could mean the side of the Post Office you would reach before the Post Office when going there from where you are now.