Hamburg's harbour and waterways lend themselves to boat trips before you even leave the city — container-port tours, Alster lake cruises, and canal trips through the Speicherstadt are all worth doing. The HADAG line 62 ferry to Finkenwerder is essentially a free harbour tour on a normal HVV ticket.
Beyond the city, the obvious destinations are reachable by train in an hour. Lübeck is the great medieval Hanseatic town — a UNESCO World Heritage Altstadt, marzipan, and red brick churches. Lüneburg, south of the city, has one of the best-preserved medieval centres in northern Germany. Bremen is a relaxed port-city counterpart 90 minutes west, and Schwerin, capital of Mecklenburg-Vorpommern, has a fairy-tale lake palace. The North Sea coast and the Wadden Sea National Park are reachable for a long day if you start early.
