Considering the fact that CUNY is the largest urban public university system in the country and the 3rd largest public university system (after the University of California system and SUNY), I would not call it small. Hunter has over 17,000 undergraduates. Almost all of the 4 year CUNY schools have over 10,000 undergrads enrolled.
Between the 64 SUNY schools and the 19 CUNY campuses, I am sure that you can find an affordable option. It may mean that you have to stay home and commute, but college is possible.
If you know that you know that you are majoring in STEM and are in the top 10% at your school, you may be able to get your tuition covered through the STEM incentive scholarship.
There are schools when you add their stackable scholarships to the need based financial aid/SUNY credits, that will cover most of the direct costs but there are no full ride scholarships that .
You will have to look at schools where you can get merit and still come within the budget that your family has set for you.