Are you going into the towns?
If so, Hamburg is fab. Definitely go for a harbour cruise (leaves from the Landungsbrücke). Speicherstadt is lovely, and the miniature museum is supposed to be great (was not finished when we lived there)
Hannover is not as scenic, a bit boring in comparison, but the Maschsee is nice and the zoo is the best in Germany. You can have a meal in the restaurant there, Meyers Hof, very typical German cooking.
There is also the Steinhuder Meer just north of Hannover which is nice.
Lüneberger Heide is good for nature friends, also north of Hannover.
And Bremen is a great wee town.
I have friends in that area, I can ask for tips for other things to do.
Food - try Vapiano in Hamburg, I think they have one in Bremen too. And Bagel Brothers are in both cities as well I think.