Bremerhaven, 65 km north on the Weser estuary, is the obvious day trip — the German Maritime Museum there is one of the best in Europe, with a collection that includes a restored WWII submarine, historic sailing vessels, and a comprehensive display on German emigration (millions left for America through this port in the 19th century). The Klimahaus, an interactive climate science centre on the harbour, is another draw.
Worpswede, 30 km northeast on the Teufelsmoor moorland, was home to a late 19th-century artists colony that included Paula Modersohn-Becker and Heinrich Vogeler. The village preserves several artists houses and studios, and the flat, wide, atmospheric moorland landscape that attracted them is unchanged. Accessible by bus from Bremen.
Hamburg is an hour away by fast train — easily done as a day trip.