Making the most of Berlin

Walk the Karl-Marx-Allee from Alexanderplatz towards the Warschauer Strasse to see what was meant to be a showcase for the GDR. Go the the Treptower Park for the Soviet War Memorial (Sowjetisches Ehrenmal) to see Russian-style victor's art. And get somewhere down to the Landwehrkanal, which runs from the Zoo to the Spree, to experience a totally different Berlin, a few metres below the streets.

I would go on some of the themed walking tours that are available, like a Cold War tour, 3rd Reich, Jewish Berlin. My favorite company is Insider Tours, but Original Walks is excellent too.

For side trips, you could go to Ravensbruck Concentration Camp. Kind of off the tourist radar, this camp was mainly for women, Communists, Socialists, Jehovah Witnesses, Prostitutes, Roma & Sinti. Have been here twice and really recommend visiting. Sachsenhausen is also recommended. Used by the Soviets after the war, many of the buildings survived. Exibits in both KZ are excellent.

A visit to Potsdam is well worth your time. You could also do a day trip to Dresden. Insider Tours offers this tour too, for about the same amount as what you would pay for a round trip ticket on the train.

The Spree Wald is near by and offers something completely different.

Have you already seen
- Köpenick castle
- the Gardens of the World
- the Botanical Garden
- Treptower Park with the Soviet Memorial
- Peacock Island

Potsdam actually deserved at least(!) two days, better three, since the city offers much more than such Sanssouci, which is just one of several royal parks. And you can do day trips:
- Wittenberg
- Leipzig
- Schwerin
- Tangermünde
- Spreewald

I second tominleiden's good suggestion for discovering Berlin. Walk from Bahnhof Friedrichstrasse to Alexanderplatz, a very busy and active place. Good suggestion on the Landwehrkanal route. If you've done typical the tourist things, I would suggest seeing Berlin-Karlshorst if you're into the history and Köpenick, the Schloss too, the city hall was famous for the Zuckmayer play, "Der Hauptmann von Köpenick" The film version with Heinz Rühmann in the leading role is a classic.

If you want to see Berlin from the S-Bahn window, I would suggest riding the S-3 line.

And don't forget the former airport Tempelhof, where two, if not three or four histories come together. In its youth it was the most advanced airport in the world, with separation of passengers, luggage and freight. In the Nazi era it was meant to be the gateway to Berlin as the imagined capital of Europe. It witnessed the Cold War in its worst days, when the Airlift kept West-Berlin alive. (The small monument at the Platz der Luftbrücke in front of the main building honours those pilots.) And now, in the new Berlin, it begins another life as a green expanse close to the city centre.

Sachsenhausen is a good suggestion, lots of information on medical "research". I don't know if you would consider Topography of Terror as a touristy thing, but it took me about four hours to go through it.

From Alexanderplatz, take the U-8 north to Bernauerstrasse and take the walk southwest along the course of the old Berlin Wall. Many interpretive stops with photos and captions in German and English. Near the end there is a Wall Museum and a bit of the Wall still standing. Ends by the old Nordbahnhof where you can get the S-Bahn back to Friedrichstrasse Bahnhof, which has its own East-West history.
English guided tours of the Reichstag building are interesting. You need a reservation through the Bundestag website.

Oh WOW! So many great suggestions! Thank you everyone so much! My wife and I have a lot to consider now.

Hi MrsEB! To answer your question.... I went on the game show The Price is Right and won the showcase. I won luggage, a car and two trips with airfare, hotel and meals included. Not bad eh?
One of the trips was to Berlin and we added a week to Switzerland as well.

Brad, that is SO COOL!!!!!! (re: winning on The Price is Right!) I've been to Berlin a few times about 20 years ago (when I was a student) but will be returning with my husband in September. This thread has been useful! The only two cents I will add (and it's not a day trip, but something that's not "typical touristy")... We are in to craft beer, and there are a few craft beer tours that look really fun. We're definitely going to be doing one of them! These are the two we're looking at:
http://www.berlincraftbeerexperience.com/original-berlin-craft-beer-tour/
http://www.brewersberlintours.com/craft-beer-n-breweries