I think there's enough to do in Hamburg for a few days, but if they want to go a bit further afield it's a quick and lovely (~1 hr) trip on the ICE to Berlin. I get the impression there are a lot of people who do it daily to commute.

Denmark - at least, Copenhagen - is just far enough to not make it worth a day trip (4.5 hrs on the ICE). The ferry takes up a lot of time, although it's by far the most enjoyable way to get between the two cities. Legoland is also about a 3.5 hr train trip away. (There are buses that go from the train station to Legoland.)