I agree with the other reviewers here - Regensburg is really a beautiful town with a fascinating history. The old town is very compact and wonderfully preserved, luckily having escaped any destruction during WW II. In the Middle Ages, many Imperial Diets (Reichstage) were held there, largely because of its strategic position on the Danube. From the end of the Thirty Years' War until the end of the Empire in 1806, the Permanent Imperial Diet had its seat in Regensburg's Town Hall. Now there is a really interesting museum there, with many original rooms.
There are also several beautiful religious buildings, especially the Cathedral of St. Peter and the Monastery of St. Emmeram, as well as the historic Stone Bridge leading across the Danube to the district of Stadtamhof, which used to be an independent city. The famous aristocratic family of Thurn and Taxis, which introduced the first postal service in Central Europe, also has its palace in Regensburg, and there are interesting guided tours. The only problem there, for people visiting Regensburg in December, is that you actually have to pay an entrance fee for the Christmas Market in the palace courtyard...