Berlin, Germany's only metropolitan world city with a lot of old and recent history and style to see, also lots of green and parks to catch your breath. You can easily spend a week there without getting bored or running out of things to do. Berlin is to Germany what New York City is to the US, the most American and the most un-American, i.e. the most German and the most un-German city in one.
Hamburg is beautiful, if slightly aloof, think of Boston.
Munich, Heidelberg, Freiburg, Bayreuth, Baden-Baden, Lübeck, Passau are all "gorgeous" medium to smaller size tourist sightseeing cities. You don't need to spend there more than a day though.
Cologne isn't a beautiful city in a strict sense, but bustles with life and has places to see if you have a good guide book. As is Frankfurt.
In the East, Dresden (a curious mix/antagonism of rebuilt trad. buildings, post-stalinist "workers' paradise" architecture and zoning plus the battle scars from the bombing raids) and Leipzig (more cohesive in architecture than leipzig) are worth a look.
If your kids are into green, the Black Forest or the countryside around Munich are good choices.
Uwe
