What do you do when you and your teenager disagree about college?
Separate your preferences from your actual constraints and label them out loud. Budget is a constraint. Wanting them closer to home is a preference. Families get stuck when preferences are presented as constraints, because students detect it and stop trusting the things that genuinely are non-negotiable.
Name the category
"We cannot spend more than this" is a constraint and should be stated once, clearly, with a number. "I would rather you stayed within driving distance" is a preference and should be stated as one. Blurring the two is the most common cause of a standoff, and it costs the parent credibility on the things that really are fixed.
Ask what is underneath
Disagreements about a specific school are often about something else: a student chasing a name for status, or avoiding a school because a friend is going elsewhere, or a parent worried about safety and expressing it as academics. Getting to the actual concern usually dissolves more of the argument than debating the school does.
Insist on evidence, not compliance
Rather than vetoing a choice, require that it be justified: run the net price calculator, talk to a current student, articulate what they would do there. A student who cannot answer those questions often changes their own mind, which lasts far longer than a decision imposed on them.
Remember who lives there
The student does, for four years. Barring a genuine constraint, a student who chose their school will work harder at making it work than one who was assigned it, and that difference tends to matter more than which of the two schools was objectively better.