The Y is always my first choice for a place to stay when visiting New York City. Any hotel less than 3 times the cost of the Y is a fleabag. Stayed at the one in Greenpoint, Brooklyn most recently that was a short walk from the train. I can live with not having a private bathroom to save a few hundred dollars a night, especially as I shower at night.
In 1992 I stayed for a weekend in the Y in downtown Chicago. Decent room, if very small, and of course I had to walk down the hall for the communal shower, but it was clean and cheap. Don’t know if it’s still there; if memory serves, it was on Butler Street.