While Leipzig is worthy of a short break itself, a little over an hour by train, it is also a managable day trip from Berlin. Plenty to do day and night, it's a city full of history, proud of it's leading role in the 1989 revolution. There's an interesting array of museums, including the former Stasi headquarters, now documenting the history of the Stasi. It also has some great nightlife with fab cafes and bars to kick back with a beer or cocktail.
www.leipzig.de/int/en/
Google map: bit.ly/QEmErh