I wouldn't hesitate to use who even in serious writing simply because it is so common. From a strictly grammatical point of view, whom will please those who insist on the object form when the pronoun is an object. It is the object of the infinitive to believe.
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AvangiI know where to go. (same sentence - no case conflict)
I'm as comfortable saying that "where" is what I know and "to go" answers the question; as I am to say that "to go" is what I know and "where" modifies it.
"To go" isn't a transitive verb. Why does it have to have an object anyway?
Why is "where" such a great direct object?