I love Berlin and I've spend a little vacation time each year for the last three years in the city, and I intent to keep going back every year!!
Ahaaa what's not to see - well Berlin is a great and relaxed place to spend a vacation - good food, easy getting around, friendly people ....
I like the former eastside the best, this is where the most famous sits are placed. One of the most famous ones is properly check point charlie - don't go there for the check point alone, if you go it must be be course you want to spend time reading the posted information on the history of the wall/Berlin in the surrounding area, or at least look at the pictures. This is a tourist magnet not really worth your time - if you are on a tight scheduled.
For information on the wall I would recommend that you go to the Mauer Documentation centre - you can see a small part of the original wall, but the most interesting part is to watch the film based on photographs from the air of the divided city in the museum building.
http://www.berlin.de/mauer/museen/dokumentationszentrum/index.en.html If you are pressed for time maybe you will find the Mauer documentation centre a little to far from the city centre.
You can also get a good impression of the wall close to the site of The Topography of Terror which is dedicated to the terror of the Gestapo during WWII. Close to this site you will see a 200-meter-long section of the “Grenzmauer (border wall) 75,” the fourth version of the Berlin Wall used from the mid-1970s onwards, stands on Niederkirchnerstrasse.
If you are not a history freak like me you ought to go see the most beautiful plaza in Berlin the Gendarmenmarkt
http://www.berlin.de/orte/sehenswuerdigkeiten/gendarmenmarkt/index.en.php.
If you are an early riser you can beat the rest of the tourist to a view from the copula of the Richetage
ttp://www.berlin.de/orte/sehenswuerdigkeiten/reichstag/index.en.php The view and the architecture is great and worth a little time standing in line. If you go to the Richetage you will be really close to the Brandenburger Tor
ttp://www.berlin.de/orte/sehenswuerdigkeiten/brandenburger-tor/index.en.php which is a "must do" site, and the holocaust memorial
http://www.berlin.de/orte/sehenswuerdigkeiten/holocaust-mahnmal/index.en.php. You can also visit the Holocaust museum at the site, but don't do it unless you are in the right set of mind - this is not really a place to go for a "good time", but the presentation of the terrible subject is excellent.
Ok if you are into shopping the best long stretch for this is the Kurfürstendamm where you will find all the international chains.
I haven't been to the Dussmann library (never heard of it must look it up sometime) maybe I should take a look at it, when I'm back in Berlin!
Enjoy your trip!
UK