Perhaps it's just me, but none of them make sense. The last part of the sentence "...go out at night." doesn't make sense with any of the choices because you have "goes" in all them, and they all don't make sense.
In my opinion, I choose the second one. moreover, I als agree that in the first one needs inversion. Like" Never does she go....". If we use this structure, our writing will be more colorful. Right?