What 2 or 3 weeks means depends on how strong you are, but any of Germany's great rivers are great touring destinations. They have great cycling infrastructure, with quiet cyclepaths (radweg), radweg-side biergartens, cheap lodging, and plentiful campings. On most rivers there are services that will move your luggage for you every night, if that's what you want.

The Rhine takes you from the biggest waterfall in Europe at the Rheinfall through the castles of the Rhine Gorge, past vineyards and flowering fields and post-industrial landscapes to one if the world's great ports in Rotterdam. Do it in reverse, and you can take a ferry from Hull to Rotterdam to start your trip!

The Danube from Donaueschingen to Budapest is one of the world's most popular cycle touring routes. You won't be lonely, but it never felt crowded. Castles and concentration camps, medieval walled town centers and great capital cities, tiny little ferries that only take half a dozen bicycles and fields of sweet smelling flowers...it's a great ride, with 3 weeks of easy days leaving lots of time for sightseeing.

The Elbe from Hamburg to Prague takes you from another of the world's great ports, where you can ride your bicycle on a tunnel under the river and ride ferries through the port, along a portion of the former border between East and West, then through smaller cities of the former East Germany. It's fascinating seeing the differences that remain, and the east is cheaper than the west.

The smaller rivers all have radweg as well, and there are plenty of hilly routes if that's what you're looking for. We hear more about cycling culture in Copenhagen and the Netherlands, but Germany has a great cycling culture as well. In summer people put panniers on their commute bikes, and take to the radwegs in huge numbers. I've spent big chunks of three summers touring in Germany, and have much more I want to explore.

The touring page at adfc.de is a good place to start gathering information. It's in German, but google translate makes it accessible. Maybe I'll see you on the radweg.

(5 years ago I bicycled Zurich to Manchester via the Rheinfall, Rotterdam, Hull, and Glasglow and a bunch of other places not obviously on the way. It was great.)