I don’t know anything specific about any Ohio colleges. However, an applicant for nursing should probably assume they need to be in the top 25% of the accepted student stats for a college, as opposed to the normal middle 50%. Most colleges provide that type of data for their whole student population. The data for accepted students can sometimes be very different from enrolled students.
You can email an admissions officer and ask about the number of applicants for nursing last year and the number of acceptances. Some colleges do post that data online, particularly if nursing is in its own “college” within a university. For example, the University of Virginia posts data for admission by school.
Just be careful that the number of the applicants vs. the number of seats can be deceiving. A university may brag they had 1,000 applicants for 100 seats. However, they may have accepted 250 of those applicants, knowing that only 100 would decide to attend that college. As students are applying to increased numbers of colleges each year, the yield for many colleges has fallen.
I found that the less well known private colleges often had the least competitive admissions. That is because their list price was 2 to 3 times the price of an in-state public, which scared away some applicants. However, the average private college discounts their tuition by 50% for incoming freshman students. Some of that is need-based aid and some is merit-based aid. Some colleges offer merit aid to a majority of their incoming freshmen, which allows parents to brag about their kids. The nursing students are often in the top 15% of the applicants of the less well known colleges, so they are often eligible for merit aid.
The most well known flagship universities seem to have some of the most competitive admissions, at least in the northeastern US. Some of those universities attract large numbers of applicants because they are known to be fun places to go to college.
Admissions difficulty greatly varies with the number of direct entry nursing programs in a region. For example, Pennsylvania probably has more direct entry nursing programs than any other state, and therefore has more programs that are not highly competitive. California has a real shortage of nursing seats.
The colleges that are further from major metro areas probably also see fewer applicants. For example, I would imagine that Edinboro University near Erie PA probably sees many fewer applicants than West Chester University near Phila, even though both are PA. state universities with similar tuition rates. Another state university in PA, Bloomsburg, sees large numbers of nursing applicants because it is not that far from population centers in New Jersey.
However, it is advisable to not go to nursing school in a mostly rural area, because you will probably need to travel long distances to clinicals. Even if the town has a small hospital, they probably will not be able to accommodate all of the nursing students. That was a major factor in my daughter’s choice of a program. All of her clinicals have been within 10 minutes away, except in-patient psychiatric was 40 minutes away.