When I was a kid, the local library wasn't anywhere near as grand as the one in Leith. But I do remember it as somewhere I spent a lot of time.
I remember the dusty book-smell of it, the shuffling, shushing quiet of it and the uneven harsh/dim lighting of it. I remember the first time I got to choose books from the "grown-up" section, and the delight of realising you could order any book you wanted. You could also read Amateur Photographer (or - ahem - just look at the pictures) and pretend you understood the jokes in Punch - all for free.
In spite of the fact that I still read a fair few books, it's a long time since I've been in a public library.