Cornell vs UVA (debt vs no debt)

$10,000 per year is at the outer limit of what a student can reasonably expect to be able to self fund with federal direct loans and work earnings during the school year and summers (i.e. no cosigned loans). If parents plus financial aid grants (not loans or work-study) cover all but $10,000 per year, then the school in question is barely in reach financially. But you do not have a lot of room for error or bad luck (e.g. not finding a job, or school work is heavy enough to prevent working enough during the school year) here.

Parents cosigning your student loan is generally a bad idea for both you and them.