Yes, Monchau looks nice but there are hundreds of places like this.
I was thinking a bit about the trip and I may suggest the following:
Stay two nights in Cologne, it is enough to see the city. What is important in Cologne is the cathedral and the relevance of the catholic church. But, for my opinion, the most meaning of Cologne is the roman influence 2000 years ago. In Cologne you may understand that Rome was not only the nowadays city in Italy but it was the world.
After two days and hopefully good nights in Cologne I would take the high speed train ICE down to Heidelberg. Heidelberg is the classy american tourist place in Germany. And I like it too. Stay two nights at the Hotel Ritter and enjoy this wonderful university city in the summer.
http://www.ritter-heidelberg.de
Heidelberg is nearly half way to Munich.
http://en.wikipedia.org/wiki/Heidelberg#1803_to_1933
In Heidelberg it is a must to drink a few beers in the famous Seppl.
http://www.tripadvisor.de/Restaurant...rttemberg.html
It is a sort of studentīs bar still frequented by members of fraternities.
Give us a feedback what you did at the end.