I didn't know where she went
This is the right one, since this was a negative affirmation, not a negative question. In the first example, you are affirming that you didn't know where she went, therefore, "did she" is incorrect. Let's suppose someone told you this: She went out last night with her friends, and you repplied: I didn't know that, where did she go? In the first clause you are affirming that you didn't know it, and in the second clause you are asking where she went, therefore, you have two clauses; "I didn't know that" and "where did she go?" both clauses don't belong to the same statement, because one is affirmation and the other is a question, but in your sentence, both clauses belong to the same statement, because you are affirming that you didn't know where she went, this is an affirmation, both clauses are affirmative.
Here are others examples of different clauses and clauses that belong to the same statement:
I didn't know where he traveled to
I didn't know, where did he travel to?
I don't know where she will spend her vacations.
I don't know, where will she spend her vacations?
In the examples above you can realize that I affirmed something, and in the others you see that I affirm something, and ask for other directly referred to the same clause, and bear in mind that comma will always be placed after the negative clause, as you can see, in order to separate one clause from the other, and to indicate to the reader that a new clause is coming.