I think it's a great idea ^•^ Making friends staying at home can be hard. More connections you will make is bigger chance you to meet new friend among them.
But public library isn't the best option. People don't really interact there. But any kind of classes, hobby club or volunteering experience is a wholesome environment to make connections ^•^
And I know, you didn't ask my advice, but old Crypty will tell ya anyways. Expectation of quick result may disappoint. Patience, respect and avoidance of drama is the best strategy to find real and nice friends ^~^
Go, get em, tiger! I believe in you