I also strongly suggest using Trains even if you go into neighboring countries.
You can buy a German Rail Twin Pass where the second person pays half price.
www.germanrailpasses.com
You can look at schedules and book individual train tickets at www.bahn.com
I lived in Germany for almost 2 years and would highly suggest seeing cities and towns that did not get destroyed in World War 2, such as Bamberg, Heidelberg and Eurfurt for midsize towns and Quedlinberg, Oshenfurt (near Rothenburg) or even the very touristy Rothenburg (40% destroyed) for small towns. Dresden, Nuremburg are nice as they have been somewhat restored of their former beauty.
Two hotel booking web sites that are based in Germany are www.hrs.com and www.hotels.de