Lubeck

It is certainly worth a detour. As a former Hansa city Lübeck has a totally different look from the usual German city. The centre if lovely, of which I only remember the P&C department store being an eyesore. When the weather is fine, you could take the train to the city's beach at Travemünde. North of Lübeck is a lake area with the small town of Eutin, which has an interesting palace.

There are numerous, if not lots of, cities/towns left out by RS in his books. Bottom line: don't rely only on RS books on German travel, especially detailed German travel and in north and eastern Germany.

Both Lübeck and Eutin/Holstein are well worth your time, Eutin I went back to last summer for the first time since seeing first in 1977. If you're into history and music, go to Eutin, see the famous Schloss (chateau), the house/museum of Carl Maria von Weber, Beethoven's contemporary. Signs point the way from the train station, none of which existed in 1977.

Lübeck is famous for its Holstentor, my first city that I visited in Germany after having arrived in Travemünde by overnight ferry.

Lübeck is a World Heritage Site, despite the destructions in WW2. As the head of the Hanseatic League it was the most important city of the Baltics in the Middle Ages, which explains the huge old town. I don't know the three week itinerary, but Lübeck is a must see if you are in the area, and without at least one typical Hanseatic town, others are Wismar, Stralsund or Lüneburg, no "Best of Germany" tour is complete.

We liked Lubeck a lot, although it has to be described as heavily touristed. We spent a night there on the way to Denmark, which is a logical route. We liked it better than Wismar or Stralsund, but those two are very different experiences than Lubeck. Since you are going to Austria, you should leave Baltic Germany for another trip. There are certainly nice cities that you're leaving out anyway, in southern Germany.