Running through train stations is bound not to be fun.
Its better than running through airports. You don't have to undergo security checks, and if you are hungry, you get a wider selection of snacks at cheaper prices. Many central European railway stations are great pieces of late 19th century architecture, and have been turned into shopping malls (see the picture of the main hall of the Leipzig central station below).
Moreover, for a trip like yours, trains should be the fastest and most convenient way of travel. High-speed trains, e.g., take you from Hamburg to Berlin in 1:45 h (from 39 € one way if booked at least one week in advance), with no check-in and check-out / luggage collection required. You start and end directly in the city centre, not some 30 km out of town. And, last but not least, there is no better way to make contact with other travellers and locals than in trains.
Long-distance night trains can be really great during the summer - my highlight was Paris-Basque country with a Georgian delegation, which ended up in a wonderful German / Georgian / Swiss / Spanish / American party. Winter sports season in the Alps should also be good in this respect ..
Seeing that your planned itinerary includes Frankfurt and Cologne, I wonder why you don't include a trip along the
Middle Rhine, either by scenic train or by
boat.
You should furthermore consider doing Hannover-Berlin by rented car, and visit the UNESCO world heritage towns of
Goslar and
Quedlinburg along the way. Hildesheim (also UNESCO world heritage), Brunswick, Halberstadt and Magdeburg are as well worth a visit, but unlike Goslar and Quedlinburg, much of their old towns has been destroyed during WW II, so they rather make for a good lunchtime stop, while I would recommend staying overnight in Goslar and Quedlinburg. The whole region was the power centre of the German empire in the 10th and 11th century, and is full of impressive cathedrals and imperial palaces from that period - something you will hardly find elswhere in Europe.
If you are interested in historic sites, you should also stop in
Aachen, half-way between Cologne and Bruxelles, to have a look at Charlemagnes throne and the coronation chapel of German Kings. Leuven, some 30 km east of Bruxelles, has a beautiful
Beguinage and is a lively university town. Conveniently, the Cologne-Bruxelles high speed train stops in both cities.
When in Berlin, you should definitely also visit Potsdam. You can do Berlin-Hamburg by high-speed train, and take a regional train from Hamburg to Lübeck. You should budget at least 2, better 3 days for Hamburg (include the weekend for a stroll on the famours Reeperbahn) and a full day for Lübeck. There are quite a number of nice places around Hamburg and Lübeck. If you intend to stay longer in the area, I can provide you wih more tips.
While Flensburg is quite nice, it is not really a "must see", so you might consider going directly from Lübeck to Copenhagen by train, or taking a
ferry to Trelleborg in Southern Sweden, and continue to Copenhagen via Malmö.
If you choose to include the Cimbrian peninsula, the most interesting places are Schleswig and the adjacent Viking townsite of Haithabu, and Ribe on the Danish North Sea coast. in that case, you should also visit the North German / Danish wadden sea coast. My favourite places are Sankt-Peter Ording (see photo below),
Amrum with its beautiful 17th century graveyard, and
Fanø, though
Sylt, Germany's version of the Hamptons, might also be of appeal to you (in that case a dinner jacket could be a good idea). In any case, one of those listed above is enough to get an idea of the landscape and of Frisian culture.
