In the website of the city of Berlin you can find a lot of very useful information about sites and museums, dedicated to the commemoration of the wall, its victims, and the GDR (German Democratic Republic, as East Germany called itself) period and works.
Among the memorial sites for the victims of the Berlin Wall you can find the Memorial for Günter Litfin, the first person to be shot and killed attempting to flee to West Berlin. The memorial is located on Kieler str. 2, and you can get there by taking the U6 to Reinickendorfer Strasse station, or by bus line 147.
There is also a memorial for Peter Fechter, an East German teenager who was shot at the crossing and left there to bleed to death. The place was marked with a wooden cross, which was replaced in 1999 by a stele created by Karl Biedermann and donated by Axel-Springer-Verlag. The spot where Peter Fechter died is marked on the ground by basalt rock.
Other memorials include the Parliament of Trees against War and Violence, and the White Crosses memorial site. For further information, including a map, look here.
Soviet War Memorials
There are also three Soviet War Memorials in Berlin, one in Treptower Park, another in Tiergarten, and yet another one in Volkspark Schönholzer Heide. You can find more information about them here, although most of it is in German.
Museums and Documentation Centers
Here you can find a lot of information about museums and documentation centers dedicated to the Communist Era, among them are:
The Allied Museum, which documents the history of the Western powers’ presence in Berlin from 1945 to 1994. It is located on Clayallee 135 – Outpost, Zehlendorf, and open daily from 10 to 18 (closed Wednesdays). The admission is free.
Marienfelde Refugee Center Museum, which is dedicated to the history of East German refugees’ flight to the West. It is located on Marienfelder Allee 66-80, and open Tuesday to Sunday from 10 to 18. They have tours there on Wednesday and Sunday at 15. The admission is free, but tours cost 2.50 euros (or 1.50 euros reduced price).
Stasi (East German secret police) museum. The name is pretty self explanatory. It is located on Normannenstrasse 22, Haus 1 (entrance) or (driveway) Ruschestrasse 103, Lichtenberg, and is open Monday to Friday from 11 to 18, and on Saturday, Sunday, and holidays from 14 to 18. The admission is 3.50 euros, or 2.50 euros reduced price.
And here is another important link from the city’s site, about the Berlin Wall History Mile, with explanation on all the Stations and topics along the way.