The center city is one of the most beautiful in the country, due to Leipzig's importance as a trade fair center which goes back centuries. Here, Johann Sebastian Bach lived for a great deal of his life, serving as Kantor in the Thomaskirche; he is buried in its choir, and the Bach Archiv across the street is a must for music-lovers. Here, also, Goethe studied as a young man, and the drunken revelry of the students in Auerbachs Keller served as an inspiration for some of the most memorable scenes in his Faust.
As you leave the train station, walk across the tram-tracks (or use the pedestrian tunnel from the second level of the mall), and turn left on Richard-Wagner-Strasse to pick up a city map from the tourist information office. Information is available in a wide variety of languages, and the friendly employees can answer just about any question.
Just wandering around the city center will show you a lot about its history. The trade-fairs used to revolve around Hofs where merchants would show their goods, and the majority of them have been beautifully restored and filled with shops. The old city hall dominates the market square, which itself is surrounded by a virtual history of local architecture, and still serves as a twice-a-week market. Behind the old city hall is the building where Germany's first stock exchange met; a statue of Goethe stands outside and the building is now used for chamber concerts. Leipzig's two churches are also of major historical importance. As previously mentioned, the Thomaskirche was where Bach premiered many of his most important works, but he was just one of several important Kantors who served there. The Nikolaikirche, with its surprising interior (pictured), was the site of the first demonstrations against the East German communist regime: although the Berlin Wall serves as the greatest symbol of the changes of 1989, it is Leipzig which deserves the credit for starting the process which led to its fall, a story which is magnificently illustrated in the museum in the Runde Ecke, the building which once served as headquarters for the regime's dreaded Stasi secret police.
Leipzig isn't all beautiful, of course: the new City Hall is an anthology of bad ideas in 19th Century architecture; it would be funny if it weren't so big. And since Erich Honecker, one of the last premiers of the GDR, went to The University of Leipzig, he paid the institution back by commissioning a huge building at its center. By current tastes it seems unfortunate that a historic medieval district was demolished to make way for this high rise edifice designed to represent an open book.
It's a good idea to time your visit so that you can get a meal or two, although staying overnight can be pricey -- and during trade fairs both pricey and nearly impossible, since most hotels are booked out a year in advance. Still, Auerbachs Keller serves great traditional Saxon fare with a light touch in its main room, and its other restaurant has superb creative cuisine, while the new Weinstock restaurant near the market is nearly its equal and considerably less expensive. Barthels Hof is one of the city's oldest restaurants and, although it tends to be popular with bus-tours, it maintains a fine seasonal menu. For lighter fare, the Kulturcafe across from the Nikolaikirche provides a good lunch in historical surroundings (it was once the church's school), and coffee and cake at the house with the elephants or the historic Zum Coffe Baum makes a good afternoon pick-me-up.
This is just a sampler of what's available in Leipzig, but if you have time for only one out-of-town excursion during your visit to Berlin this is probably the best value for your time and money. And if you live here and haven't been yet, what's keeping you?