The old and the new Berlin are both exciting places to go to. Famous for the historic Berlin wall, the old side of Berlin is worth a visit. Please do not expect that this wall will be huge. If you actually read the history, it has been demolished and few blocks could still be seen in this area. Check Checkpoint Charlie on this side of town too. Its the crossing point between East and West Berlin.
Since this place is historical, try to visit the Museum Island where there are 5 museums. Spend half to full day in these clustered museum. If you want more history, you could also visit the memorial for the Jews in Europe.
Viktoriapark, although kinda far is popular amongst the locals for hangouts. While the Tiergarden is vast and good for hiking. Bradenburger Tor is a nice landmark you should have a photo in. The gate has has great history. Berlin’s shopping malls are also a good exercise because they are big.