There are not many places in London like it. On a Saturday during market hours it heaves with stalls and visitors for a good mile or two. Great place to pick up some bric-a-brac, genuine oddities and a great bite to eat, or just enjoy the hustle and bustle vibe of the place.
It's a members-only library but you might be granted access with a research request. The writer's room is great but there's a few special, hidden corners among the bookshelves to tuck yourself away in.