Does financial aid (FASFA) cover out of state tuition?

So I think you are kinda misunderstanding what FAFSA is. FAFSA stands for Federal APPLICATION For Student Aid. The primary way the federal government gives aid is through pell grants which almost exclusively go to families that make under 60K AGI/year. The average pell grant award is in the low 4Ks. Are there public schools where the difference between instate and out of state is 4k absolutely! But its not super common. I still recommend filing the fafsa as the institutions themselves primarily use fafsa to give aid to its students. Also private colleges do use FAFSA and sometimes also uses in conjunction with the CSS profile.

Private schools 99.9% of the time are more expansive than a similar public school (sticker price) BUT they award more aid so it kinda counterbalances.

Hope this helps and please comment if you'd like clarification as Id be happy to help!

If you know that financial aid will help pay for the fees of private schools you may attend, then definitely apply there. If you have any scholarships or arranged payment with another party, I would recommend applying to public schools as well. You could always turn down a school if you end up getting into a private one that is financially covered, but it's better to have options.