These are not necessarily books where the City becomes a character in itself, although that does happen with a few of them, but these books are set in these locations and remind you of those cities.
Dublin – Ulysses, The Dubliners
St Petersburg – Crime& Punishment
Kiev – The White Guard
Stockholm – The Martin Beck Series
New York – Catcher in the Rye
Chicago – The Jungle, Sister Carrie
Paris – The Maigret books
London – Dickens
Brighton – Brighton Rock
Tokyo – Norwegian Wood