So here’s my situation: neither of my parents went to college, but my aunt went to Stanford. If I were to apply there, what should I put down?
You’ll be able to indicate in the parent section that neither of your parents went to college. I’m not sure if the Stanford app asks specifically about what family member is the legacy - if there’s somewhere to add that it’s your aunt, definitely note that to avoid confusion. Someone in the admissions office could also advise you on this!
I’ll have to call them. Thank you! 
They don’t care that your aunt went; most colleges ask about parents and siblings, some ask about grandparents, very few count other relatives and it wouldn’t really impact anything. It’ll matter way more than neither of your parents graduated from a four year university.
Aunt won’t help. But you can mention her in an essay. Stanford turns away many true legacy applicants as it is. They only guarantee that the legacy will have 2 readers, no additional preference. (Huge donors are in as different category. )
First generation is probably a more powerful hook than legacy, anyway. Most schools are trying to increase their number of first generation students.