Since you plan to study EE, if it is ABET the school name isn't as important in industry or landing funding for post graduate education. University of Toledo for example had 100% placement and average starting salary of $63,453 http://www.utoledo.edu/Programs/undergrad/Electrical-Engineering The cost of living index between regions accounts for the difference in starting salary averages rather than prestige of institution since most graduates will pursue employment within the region. You would qualify for substantial OOS merit there and they are one of 8 engineering programs that require a co-op, so their career services office is top notch and you would have ample opportunity to earn what you need and possibly graduate debt free. They place students across the country. You'd also have a huge financial advantage over the other students since presumably you would be able to live rent free during your co-ops in an area that pays well if you sought opportunities near your parents' home. If you are still looking for a safety school consider it.
60% of students receive aid
Average Grant Aid $28,179
So on average, students are coming up with $40,000 each year whether it is loans or cash to attend.
Is the OP an exceptionally strong candidate in the 99th percentile of NYU applicants with a shot at full ride, or an exceptional hs student and average NYU applicant?
"Cincinnatus is not just another scholarship program. With its focus on community service while enrolled, students turn their unique experiences, aptitudes, and abilities into a quality education at the University of Cincinnati."