What state ARE you in?
Some states have academic common market agreements with other states for majors they don’t offer at their own public universities.
It’s really impossible to help you when all we really know is that you want to go to college in NYC or Boston.
At this point…this isn’t even a financial aid question. Unless you have some affordable college that you didn’t mention here…none of these appear to be affordable for your family.
Parsons, IIRC, would cost you at LEAST $30,000 a year in loans. That’s a LOT of loan debt. You can’t take that yourself. You would need a cosigner for ALL four years.