Four days in Leipzig: Bach's church, and the one that brought a state down

Start where Bach worked. He took the job of cantor at the Thomaskirche in 1723, stayed until he died in 1750, wrote most of the cantatas and both surviving passions in that time, and was buried in an ordinary churchyard and moved into the chancel much later. The bronze slab in the floor near the altar is where he is now. The boys' choir he directed was founded in 1212 and still sings here twice a week.

Two minutes away is a coffee house that has been serving since 1711, one of the oldest anywhere in Europe, with a small museum of coffee upstairs and three floors of rooms Schumann and Wagner drank in. It reopened not long ago after a long restoration.

For the evening, find the arcade off the market square. The Maedlerpassage was built in 1914 in glass and marble, and the stairs at one end go down into a wine cellar that has been in business since the sixteenth century and that Goethe, who studied law in this city and drank here, put into Faust. Bronze figures of Faust and Mephistopheles stand at the top of the steps, and the students' boots are rubbed shiny.

The Nikolaikirche is a plain Gothic box from the outside and a startling thing inside: remodelled in the 1780s in pale pink and green, with columns that open into carved palm fronds at the top. From 1982 it held peace prayers every Monday at five, which drew a slowly growing crowd of people the state could not easily arrest for praying.

On 9 October 1989 the crowd came out of that door into a square with armed units, water cannon and hospital beds prepared across the city. Roughly seventy thousand people walked round the ring road holding candles. Nobody fired. Within a month the government had gone, and the phrase people here still use is that the revolution was made with candles and prayers.

Two minutes west is the Round Corner, the district headquarters of the Stasi, kept as a museum by the citizens' committee that occupied it in December 1989. It is deliberately unmodernised: original offices, the smell samples in sealed jars, the machines for steaming open post, the paper shredders they were still using when the crowd arrived. Then finish at the contemporary history forum on the market square, which is free and tells the whole East German story from 1945 to reunification.

The Museum der bildenden Kuenste stands in the middle of the old town in a glass block that replaced the bombed original: five centuries of painting, strong on Cranach and the Dutch, with rooms of Max Beckmann and Max Klinger, and a good contemporary section including the Leipzig painters who made the city's name in the art market twenty years ago. Two hours.

In the afternoon take the tram west into Plagwitz, which was one of the first industrial suburbs in Europe and spent forty years falling apart. The canal cut through it in the 1850s to serve the factories is now a towpath with cafes on it, and the streets are a mix of restored brick, scaffolding and gaps.

The Spinnerei is the reason to come. A cotton mill that once employed thousands now holds a dozen galleries, a cinema, a hall for large installations and the studios where Neo Rauch and the painters around him work. Nothing is polished, entry to the galleries is free, and an afternoon disappears easily. Check the day: most of it closes on Sunday and Monday.

Tram 15 runs south east to a hill of granite in a park. The Battle of the Nations monument was finished in 1913, on the hundredth anniversary of the battle it commemorates, and it is 91 metres high, deliberately more mountain than sculpture. Beneath it in October 1813 the armies of Russia, Prussia, Austria and Sweden broke Napoleon over three days, in the largest battle Europe had seen before the First World War, with about a hundred thousand casualties.

Inside is a crypt with sixteen stone death masks, a hall of colossal seated figures, and a narrow spiral stair to a platform at the top with the whole city on the horizon. It is grim, imperial and completely unlike anything else in Leipzig, which is the reason to see it.

The tram back to the Hauptbahnhof takes about fifteen minutes and drops you at the door.