About one hour outside of Berlin is the Sachsenhausen concentration camp memorial. Under Nazi Germany, the concentration camp was used first as a work camp for political prisoners until eventually it was expanded and enlarged to also include facilities for mass murder. After WWII, Sachsenhausen was briefly used by the Soviets to house Nazi prisoners of war where many died.
The Soviets originally erected a monument to those that had lived and died at Sachsenhausen concentration camp at the end of the 1950s. After the reunification of Germany in 1991, additional museums and educational facilities opened at Sachsenhausen (including the memorial in the photo above). Today, the site is a chilling memorial to the prisoners who lived and died there. An interesting fact: Sachsenhausen was one of the sites of the largest mass murder of homosexuals during Nazi Germany. This was due to its proximity to Berlin, which had been a fairly liberal and open society in the 1920s.
The site is free and open to the public, in addition to being easily accessible from central Berlin. Take an S-Bahn train (line S1) from central Berlin in the direction of Oranienburg. Disembark at the Oranienburg station. You can walk the 2km from the station to the former concentration camp (which is marked with signposts). It's possible to spend several hours at the site, as there are several museums and exhibits.