Not a comprehensive list in any way, but two suggestions off the top of my head: one large school and one small school.
U of Cincinnati is a large, urban, public university that’s known for inventing co-op education. It’s known for strength in majors as diverse as Industrial Design, Nursing, Engineering/CS, and Musical Theater. Also in the mix is a surprisingly prominent Classics department: https://classics.uc.edu/ For undergraduates, they offer two majors, Classics and Classical Civilization. The full-pay cost of attendance for international students is just over 50K/year, and the maximum International Outreach Scholarship is 15K/year, so getting to your budget is possible.
In contrast, Kalamazoo College is a small liberal arts college (just over 1200 students) in a charming small city. They have a flexible curriculum that allows students to customize their majors, and they are generous with merit aid, so quite likely to get to your budget in my opinion. Their Classics department offers four different majors, which is pretty impressive in such a small school: https://classics.kzoo.edu/
Would you qualify for need-based financial aid? If so, there may be options among schools that offer need-based aid to internationals (although most either don’t guarantee to meet full need, or make need-aware admissions decisions).
But the two I suggested have potential to get to 40K or below on merit aid alone.
I’m sure there are more good possibilities, but comparing these two very different schools would be a place to start.