Your extracurriculars would be valued at Ohio State. Apply EA and admission is likely. On a $20,000 budget an oos applicant needs to win a Morrill (EA preferred, must apply for Morrill) or Eminence (must apply by EA, indicate honors and apply to Eminence) scholarship. On an affordability front that would make it a reach since it is tough to get those awards, but worth your time to apply since you’d be a contender.
If your parents are willing to pay more you’d only need to receive the National Buckeye (no additional application, all admitted oos students considered), which I think is likely. So if they do bump up the budget, Ohio State would be a match.
The student newspaper is The Lantern, there is a living learning community called the John Glenn Civic Leadership Community that might interest you and a good College of Public Health.