People in NY may not call it CUNY. Their kid goes to Baruch. Their kid goes to John Jay. Their kid goes to Macauley (an exceptional honors program). These are all part of the CUNY system but are independent colleges. According to the NY Times, "CUNY propels almost six times as many low-income students into the middle class and beyond as all eight Ivy League campuses, plus Duke, M.I.T., Stanford and Chicago, combined.”
It is hard to be a taxpayer in NYC and NOT have heard of (or know someone who attends/graduated from) one of the CUNY’s but they have their own names, campuses, identities, and academic programs and specialties.