To get an overview of Berlin sights you could do a walking tour. Brewers, Insider or Berlin Walks are just some of the companies who offer a tour.
If the weather is nice you could do boat trip which is nice way to spend a few relaxing hours plus you do see a few sights.
Brandenburg Gate, Checkpoint Charlie, Reichstag building (go early or late to avoid queues & it’s free!) are easily done on one day together with a river trip which is surprisingly good – the one-hour one is cheap and probably enough for a flavor.
Sanssouci at Potsdam is a bit of a haul out of town (and you need the C zone travel ticket), but very impressive. If you decide to do this, I’d recommend a tour from the centre, more expensive, but easier than working out buses etc. from Potsdam station.
See the East Side gallery with a stretch of the wall. Use Ostbahnhof.
Other things worth doing are going to one of the many cafes who offer breakfast, especially nice are the breakfast buffets who are offered at many cafes on Sundays.
You can get a Welcome Card which will allow you to travel on the public transportation for 3 days, cost 21E This is for zones a and b.
The Museum Card is 15E and allows you entrance to many of the top museums in Berlin. if you purchase these two together you save 3E. The Welcome card also gives you discounts on many things in Berlin. I did two walking tours and saved 3E on each. I also saved a few E on entrance to the Berliner Dom.
There are some companies that offer bike tours of Berlin that sound like a lot of fun.
The Pergamon Museum, has the Pergamon alter, The gates of Ishtar,
The Altes Museum, worth going to see the bust of Nerfitti
The Hamburger Banhoff Museum, Berlins modern art museum. I really liked this museum.
The Helmut Newton museum, Great Newton exhibit and Lachapell exhibit as well.
These were all covered by the museum card.
The Reichstag, I would definitely go up in the dome. There is generally a line, but if you get there early in the morning(I went at 8:30) of later in the evening there isn’t really a line.
The Memorial to the Murdered Jews Of Europe, This was incredibly moving. More so once I walked through it. The information center underneath was very moving as well.
The East Side Gallery, this is the largest section of the Wall still standing. It was painted by artists from all over when the East German government fell. I am so happy I took the time to go here.