We're heading back west to visit the Rhine and North Rhine-Westphalia (NRW).
Taking a Rhine cruise is enjoyable in nice weather. It runs the whole way from Mainz to Cologne, but you can get on or off at any of the stops in between. The Mainz/Rüdesheim to Koblenz stretch features castles galore, the remains of various kingdoms, fiefdoms, and assorted people who wanted to collect taxes from people traveling down the Rhine. The hostel at Bacharach is inside one of them. (Reserve well in advance if you want to stay there, and be aware that it's often filled with groups of schoolchildren.)
NRW borders both Hessen and the Rhineland on the south. As you may guess from the name, the Rhine flows through. The Ruhr, Ems, and Weser do as well. The southern and southeastern region is mountainous, but the northern part is flat lowlands.
The one city I've been to in NRW is Cologne. There's not a whole lot of interest in Köln, but there's a famous cathedral. It's easy to find: go out of the train station (following signs) and look up. Marvel at its size, take a tour. That's about it.
The former capital of West Germany, Bonn, is also in NRW. Beethoven spent some time in Bonn, and there was an elector of the Holy Roman Empire based there. There's a palace you can tour.
Münster is in the northern lowlands, the Münsterland. It's home to a Romanesque/Gothic transition cathedral, a castle, and a university.
Aachen (Aix-la-Chapelle, for the Francophiles) is in far western NRW, somewhat near to Köln, by the border with Belgium and the Netherlands. Charlemagne (Karl der Grosse) built a mansion there, and Otto I was crowned Holy Roman Emperor in the cathedral Charlemagne ordered built, as well as subsequent Holy Roman Emperors.
The Ruhrgebiet is in west-central NRW and is the largest industrial-metropolitan area in Germany.
Düsseldorf has a lot of culture and nightlife, and I'm told it's more interesting than Cologne.
Next up: probably Niedersachsen/Lower Saxony.