What kind of aid to expect?

Ditto. Yes, @1650mile, I know you said you want to apply to top schools “out of state” - but your list has to include your in-state options, and it would be helpful for us to know what those options are.

Also, at which “large research university” is your dad a professor? If his position at that university can get you a reduced cost, that’s also something you need to consider. If you give us the name of the university, we can help you figure that out.

Finally, as mentioned above, your dad’s affiliation with University X may also get you reduced tuition at other universities, through what are called “tuition exchange” programs: University X lets faculty children from University Y attend at a reduced cost, and University Y does the same for faculty children from University X. And the list of universities participating in the program may include several “top” schools!