I have been to my library yes. You don't need ID or a library card (unless you want to check something out or use a computer) and you can pick up any book you like (including e.g. 50 Shades of Grey), sit down at a table, and read it. There are children in there all the time and there isn't an adults-only section.

A minor can walk into any library I've been to, grab any book off the shelf, and read it.