We will be in copenhagen for a few extra days and would like to take the train to Germany. Any ideas on where to go - preferably a smaller city?
Not small, but Hamburg is a beautiful city with two lakes within the city boundaries as well as a busy and welcoming seaport.
Good food, especially seafood, and nice walking areas.
A boat tour around the harbor is a fine adventure..
If you want a city smaller than Hamburg, which is a big city and cultural center of North Germany, then I would suggest Lübeck. If you want some place north of Hamburg, even smaller, going into the Holstein area, I suggest Eutin, esp. the Schloss.
Hamburg is the second biggest city of Germany, so probably not what you are looking for. But the train to Hamburg also stops at Lübeck, which is smaller, mostly preserved and a Word Heritage Site. From Lübeck you could do day trips to towns like Wismar, also a World Heritage Site, Schwerin with the Neuschwanstein of the North, or Ludwigslust.
Or see the Baltic coast, which is the most popular summer destination of Germany, with everything from beautiful old towns, Gothic brick churches or nostalgic steam trains to posh spa towns, cozy villages and perfect, miles long beaches. But getting there is a bit more difficult, sicne you either have to take the train to Gedser, and from there the ferry to Rostock, or the train to Hamburg, and from there to Rostock. This journey takes at least 6:30h, compared to 4h to Lübeck. But if you travel between May and September and stay for longer it's worth it.
I realize you said "preferably smaller", but thought I'd throw this in regarding Hamburg.
This summer, we are using Hamburg as a 2 night stopover after a week in Berlin prior to taking the ferry-train to Copenhagen for several days. We initially thought this would just be a :we can find somethings to do", and now I am sorry we won't have an additional day there. I fear the International Maritime Museum on its own may fill the full day there and not leave us much wandering time. Depending on your interests there is much to choose from.