Have you considered Iowa State? You can figure out whether or not you would be admitted using their online admission index calculator.
Their scholarship aid is also predictable. Freshman Awards - New York - Office of Admissions
Ohio State has a CSE degree in their college of engineering, but also offers degrees for CIS in their college of arts and sciences. The major classes are all taught by the same department and uses the same career office. Since the university does not admit by major you would just need to be admitted to the university and could apply to their college of engineering later if you decide you want to pursue CSE and aren’t directly admitted to that college. The scholarships are not automatic, which might work in your favor since you have a very good SAT score. If the National Buckeye scholarship would put you within budget, it would be worth applying. Merit-based scholarships - The Ohio State University