Really, though, the most logical and sensible day trips from Berlin are those that lie on the extended city Network, specifically on the S1 S-Bahn train line

Potsdam is about an hour and a half taking the S-1 toward Wannsee. It's a real quick walk to Park Sansouci, and then you just wander around. The gem, of course, is Schloss Sansouci, the summer palace of Frederick the Great (and where he is buried, not with his wife, but with his dogs). Read up a bit on a court that the Bach family played at – and that was the Versailles, and then some, of Germany. Also the location of the Potsdam conference from 1945 is worth visiting, if you are a history buff.

In the other direction, but literally and figuratively, onothe S-1 is Oranienburg, the location of the Sachsenhausen Concentration Camp. For me, Sachesnhausen, with it's extensive exhibits, and partially extant crematorium, was at least as moving as Buchenwald. If you've never been to a Nazi Konzentrationslager, you owe it to yourself to visit one once. And Sachsenhausen is a good one to visit, and very accessible from Berlin.

Dresden is do-able, but you'll spend a lot of time on trains. If you do, go early, and return late. It's 2 and a half to three hours by train. Hamburg is faster, 1.5 to 2 hours, so do able.

I'll also point out that Berlin has more than enough to fill 4 days. Indeed in 2005 I was in Berlin for a month and did not see everything I wanted to.