Berlin in one day
Realistically ambitious. Route: Alex → Museum Island → Berlin Cathedral → Unter den Linden → Brandenburg Gate → Reichstag (book the dome in advance!) → back by S-Bahn.
TV Tower in the evening if time permits – the sunset view is worth the extra hour.
Weekend in Berlin (2 days)
Saturday: route as above, plus Holocaust Memorial and Potsdamer Platz. Dinner: Prenzlauer Berg or Kreuzberg.
Sunday: Museum Island in depth, afternoon East Side Gallery, evening Hackescher Markt.
Three days in Berlin
Day 1: classic Mitte.
Day 2: Cold War and Wall history (Checkpoint Charlie, Topography of Terror, East Side Gallery, Mauerpark).
Day 3: Prussia (Charlottenburg Palace, Kurfürstendamm) or Kreuzberg/Neukölln for the alternative scene.
Berlin with kids from the Alex
LEGOLAND and SEA LIFE are 15 minutes on foot. The DDR Museum works for teenagers too. TV Tower obviously. Berlin Zoo direct on the U2.