The Stasi Museum is absolutely, utterly, brilliantly barkingly mad yet fascinating. Loads of stuff from the old DDR days including all the stuff the secret police used to spy on people. Some of the rooms have been left as they were which is amzing too. Its not too far from the centre, if its ok walk down Karl-Marx Allee which has some brilliant architecture.
To be honest, as horrifying as it is, you would be missing out if you didnt visit the concentration camp at Sachsenhausen. Get the train to Oranienburg and its about 15 minutes walk. Dont bother with the tour, just wander round and get lost in your thoughts, its very moving. The Holocaust memorial just off Brandenburg Gate is quite incredible too. If you are still up for more, the Topography of Terror is a fascinating museum too.
The East Side Gallery is worth a visit too. Have a wander round Tiergarten, to be honest I can just wander round Mitte and that area in the East all day drinking coffee and stuff.
There are some good cheap restaurants on Oranienstrasse, mostly pizza and italian but ok. Currywurst is good, get amongst it.
I’ll be honest, Mauerpark was lost on me. It was a good day so we just sat and had lunch in the park but all the stuff on sale was tat you would find at any market.
Stasi museum
Sachsenhausen