I've just returned from my 3rd trip to Berlin, and I have to say that it gets better every time I visit it. Cutting-edge cool and palpable modern history combine to produce a gritty, vibrant yet relaxing city. Modern architecture sits seamlessly alongside a church missing half of it's roof after being destroyed by a WW2 bomb. There are literally days worth of historical sites to see: The Berlin Wall, Reichstag, Brandenburg Gate, Topography of Terror & Checkpoint Charlie being some of the highlights.
In 2004 Berlin's mayor Klaus Wowereit declared "Berlin ist arm, aber sexy" - Berlin is poor but sexy. This still holds true today with the city being very affordable by European capital city standards. It's one of the most cycle friendly cities I've ever visited, with extensive off-road bike lanes criss-crossing the city. In addition, almost a fifth of the city is green space dotted with approx. 2,500 public parks and gardens.
If you're in Europe and looking for a city break for 3-4 days, you could do a lot worse!