Berlin

The history here is staggering: start with the ancient Pergamon Altar, and recall that the first wave of great archaeologists were all German. Zip a few thousand years forward and you'll see the scars of WWII -- a bombed out church here, bullet holes there...and then catch a few remaining sections of the Wall and explain to your kids that we all thought this thing was permanent. Until it wasn't.    

Are your kids old enough to appreciate good music? Throw some Berlin-inspired tunes at them. David Bowie to start, perhaps (careful selections, of course). Throw in some Lou Reed. And finish with Achtung Baby. Keep an eye out for an old Trabi while you're at it.    

For all that: Berlin is energy and activity, it's a sprawling modern metropolis with anything you want in a big city, at your fingertips. Find it, and meet it head on, like a Berliner.    

It's not too far from Bavaria, and cheap intra-Europe flights will get you to Hamburg, Paris, Rome, or Barcelona.