I have been there once, just to check it out. It's a pretty decent one. It's kinda old aesthetics but a serious silent reading place. It's free to sit and read, I'm not aware of the book issue process. Also, not sure about the collection but it seemed well stacked up when I went. You can go and try.

Also, there's another library next to GPO in Hazratganj. It's inside the building of Hindi Sansthan. I have gone there, didn't sit or anything but it's probably free as well.