It is not that CUNY does not have housing, it is the fact that CUNY housing is expensive. Dorm cost range from 12-17K a year depending on campus. Then you must factor in food (which can also be expensive and transportation- if your son wants to leave the neighborhood).
https://www2.cuny.edu/current-students/student-affairs/student-life/housing-residence-life/highlights/
https://www.1kenilworth.com/layouts-pricing-amenities.php
OP should also look at Fredonia, not a safety (GPA is 90 but SAT is 1120)
https://www.fredonia.edu/academics/colleges-schools/visual-performing-arts
There are BA in musical theatre at Cortland and Geneseo (academically a reach)
BFA programs at UB (academically a reach)
OP, please be reminded that Excelsior has been a game changer for many middle class families (125k and under). As a result all of the SUNY and CUNY schools are having an increase in applications making them more competitive for admissions because they are now more affordable (if family gets Excelsior and student takes his federal loan, it can be doable for a 12-15k, where in the past family in this income range was full pay.
As I previously stated, if your son is not financially or economically disadvantaged (eligible for SEEK) it is going to be an uphill climb for general admissions in City and Bklyn.