Our local Library (the Malthouse Library in Abingdon, Oxfordshire) has been a favourite haunt of ours for a few years now, even before Charlotte was born. Spread across two floors, the majority of the ground floor is taken up by a massive children's section going from baby books right through to teenage stuff.
Thankfully there are hundreds of toddler books to choose from and so far we've managed to avoid being stuck for something to read.
The library's staff are always friendly and helpful, and on wednesdays (which I fortunately get to spend with Charlotte) they run a couple of nursery rhyme singing groups, dishing out noisy instruments so that babies and toddlers can sing along and join in making a glorious racket.
The library also has a pretty huge fish tank (with very few fish left in it, alas) and plenty of comfortable seating and toys to keep little ones occupied.
We're extremely lucky to have such a valuable resource so close to home.
Site Link: Abingdon Library