Finances and budget should be a top factor in choosing a school. Sounds like your parents can pay $20k per year, and you can take $27k in total over the 4 years of undergrad. Will you qualify for need based aid?
Have you run Cornell’s Net price calculator? Please do that so you get a cost estimate, and can see how much need based aid you will get. (You should run NPCs at all your schools).
Any loans above the student loan each year will be on your parents either directly or as a co-signer.