In high school I applied to two large state schools, Wash U St. Louis and MIT.
Didn't get into MIT, WUSTL only gave me a bit of work study (5-10 hrs / week) which isn't really aid because it is a job. Would have cost me 50k/ year to attend excluding room & board.
Both of the state schools gave me academic merit scholarships plus one school gave me some financial aid. Would have cost about 15k / year at one state school and 8k / year at the school that I ended up attending. My scholarship was guaranteed for 4 years if I maintained above a 3.3 or something like that plus I earned additional scholarships as an upperclassman.
I was also able to graduate in 3 years because the school took lots of AP credits. I participated in undergrad research every single semester (got paid $10/ hour too) and had a paid internship each summer. Profs always replied to email quickly, were willing to talk after class or at office hours.
State School
2x8k + 1x 6k (had extra scholarships last year) = 22k
WUSTL
4x50k = 200k
Saved a ton of money and from talking to friends private schools costing the same as state schools seems to be kind of a myth (people will count things like subsidized loans and work study as scholarships and aid when they really aren't)