We did exactly this at Easter last year - case of German GCSE revision (tick), History: Cold War/Rise of Wiemar Republic revision (tick). We got a very good deal with BA (flights, 4* hotel, b&b for 4 nights for less than £250 each), hotel just down from Checkpoint Charlie, arriving Saturday evening, back Wednesday morning. Sunday we walked to the German History Museum (Deutsches Historisches Museum) which has a huge section given over to the Wiemar Republic and then the Cold War, then walked down to the Brandenberg Gate, across to the Jewish Memorial, over to the Reichstag, back to Checkpoint Charlie and the hotel. Monday we went out to Spandau and then back to Charlottenberg (though the palace is closed on a Monday), walked across Tiergarten taking in various sites such as the Russian memorial, then to Potsdammerplatz for supper, then Tuesday we did Museum Island, went up the Fernsehturm Tower which gives you a really good view of the city, had great pizza sitting by the river, then flew home on the Wednesday morning and back home by lunchtime.
Berlin tube system if terrific and easy to work out and otherwise we just walked and walked and walked and got a real feel for the different zones and how it was divided post '45. We were very impressed with it and want to go back. DS wants to do German at uni and really wants to be in Berlin in his year abroad.
The one thing we would like to have done and couldn't was the Reichstag - it was closed for work on the dome when we were there. You do need to book and you need to take your passports with you if you do go - security is very tight. That's something to do on a return trip for us though.
Well worth getting the DK Eyewitness Top 10 Berlin guide. We found that really helpful for planning and had a good map too, though we got a bit lost on all the paths in Tiergarten and my ds was a little disconcerted by the sunbathing nudists! You don't get that in St James's Park...