CUNY is cheapest, agreed, and it’s also surprisingly good. Look carefully at what each school offers. I disagree that you should only look at schools in your family’s borough. There’s excellent public transportation in the City and, barring the most far-flung commutes, you can do well by traveling to other boroughs.
Note that if your commute would take place mainly on an express line, that simplifies things a lot. Express trains include the 2, 3, the A, D, and E, and others.
Check out the Macaulay Honors college. If you’re OOS, it might be slightly more than free, but if you’re considered in-state then it’s free plus a stipend plus a place to live.
deadline is DECEMBER 1.