Another option for rolling Admissions is Manhattan College.
Manhattan is smaller (I think 3,000-4,000) but has a campus and it is literally in NYC. They still are accepting applications. They are an interesting combination of STEM and liberal arts and Engineering. I know several people who graduated and they are very smart people.
Manhattan doesn’t have neuroscience as a major but you could combine Math and Bio. One of the math professors is coincidentally a Pitt Nueroscience PhD and does computational Neuro work.
The school is in the middle of making changes to their programs to add more health programs like nursing and other majors. That works in your favor because I think it turned off some liberal arts majors.