But, biryani, I don't want a toddler and baby group, I want somewhere I can take my toddler and she can learn about how much fun books are. If the library was a silent solemn place I wouldn't feel comfortable taking her there at all, but a playgroup or park isn't going to have masses of board books at toddler height that she can pull out, plop down on a cushion, and "read" to herself upside down, is it?
I love my library. The kids section is down one end and has low sofas and a few quiet toys (wooden puzzles, mostly), and some teddies, and loads of books. I read the MumsNet Guide to Toddlers there, while my daughter practised walking by holding onto the bookshelves. Then there's the cafe/magazines bit, which is slightly quieter than the kids bit, then the checkout desks, and the other side of that is the adult section, which is pretty quiet.
When I was a student I could never concentrate without total silence, so I do think academic libraries should have some silent bits. But local libraries are vibrant and fun and providing internet connections to people who don't have them is a public service. Arguably, these days, it's at least as important as providing free books.