Hamburg's history museum has lots of kid-friendly features: it's chock-full of intricate ship models, has a large model train set (which runs on the hour), and is home to the actual bridge of the steamship Werner, which you can clamber over. As it chronicles the city’s evolution, it reveals titbits such as the fact that the Reeperbahn was once the home of rope makers (Reep means ‘rope’). There is a good exhibit on the history of the city's Jewish population.
Museum für Hamburgische Geschichte
St Pauli & Reeperbahn