Oh, I wanted to write the same thing. Hamburg and Lübeck.
You can research your train connection on www.bahn.de (although I'm not sure you can buy your ticket there, since both the start and end points of your journey are outside of Germany). And you can have the details of your trip displayed, and in the next step, you can have all intermediate stops displayed. This is very convenient if you'd like to stop "somewhere", but don't know yet where.
How about your luggage? Maybe you could visit all three cities, Bremen, Hamburg and Lübeck. You don't have to stay overnight there. You could lock your luggage at the station for a couple of hours, if it's not too large. What I'd do: Go to Bremen in the morning, lock your luggage at the station, proceed to Hamburg after a few hours, spend one or two nights there. Then, go to Lübeck the next morning, lock your luggage at the station, do your sightseeing, and proceed to Kopenhagen in the evening.
When in Lübeck, don't forget to see the Holstentor. This is really famous because it used to be on the 50 DM bill.
And let us not forget about marzipan! Lubeck is famous for it!!!!
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