Not only Berlin itself, but also its urban hinterland is very appealing. Go day-tripping to get a picture of it and visit:

 

Schloss Rheinsberg (Rheinsberg Castle)

Schloss Sanssouci (Castle of Sanssouci)

Potsdam/Holländerviertel (Dutch Quarter)

Kloster Lehnin (Lehnin Abbey)

Wandlitz

Spreewald (Spree Forest)

Scharmützelsee (Scharmützel Lake)/Bad Sarrow

Belziger Therme (Belzig Thermal Bath)

Müritzsee (Müritz Lake)