Chetham's Library is the oldest public Library in the country. You'll find it between Manchester's Anglican Cathedral and the museum that was URBIS and will soon be the National Museum of Football.
I spent a pleasant hour in their reading room, perusing an essay about the emotion of crime in broadside ballads between 1500 and 1800.
What a lovely place! It's now part of a private music school that you can't wander around sadly, but the library itself is well worth a visit if you have nothing better to do.