There is so much to see in Berlin itself that it's only worth doing a day trip outside of Berlin if you are there for a week or more.
Nice places for a day trip are for example Potsdam which can be easily reached by public transport. You could also spent a day in Waren an der Müritz, Rostock or Warnemünde. Depending on when you'll be in Berlin you could also spend a day in the Spreewald. Spreewald is best visited in Spring or Summer though.
Dresden is pretty nice but you should spend there more than just a day.
Dresden is really worth visiting. With the fast train IC/ ICE you will need about 2hrs to get there.
Get off at Hauptbahnhof (Main Train Station) at walk along "Prager Strasse" - kind of the famous shopping street. It will lead you to the "Altmarkt" with the "Striezelmarkt" (christmas market). Further on you'll get to the OLD city with "Frauenkirche" which recently was rebuilt and all the other builings which are really nice and to the "Terrassenufer" which will give you a marvellous view on the river Elbe and the city.
Have a look on this page: www.dresden-online.de
Enjoy your time in Germany
Thanks a lot for your help, it´s very useful.