@the_black_jew, right, not all of them have one. Ys with one can be located via their website:
https://www.ymca.org/find-your-y?distance=175&type=branch&facilities[]=75
About 16 years ago when my spine collapsed and I was relearning how to walk, I joined the Y down the street from me to use their pool as part of my rehabilitation and they had a climbing gym that they had recently built. I’m not sure if they still do this but at the time, the Y gave a discount on membership fees for those who were disabled and low income.