I'm afraid I will not second the raving reviews below. However I might just have caught Bamberg on a bad day: there were streams of tourists milling around (some of them even aboard pseudo-Venetian gondolas), a number of stag/hen parties, some drunks occupying park benches, a couple of homeless. I even encountered a loud group of whom one person used the Nazi salute. There's a jail sentence for that in Germany.
The city itself reminded me a lot of Strasbourg - its riverside location, typical German construction style and the cathedral. But of course, there are some worthwhile things to see. The former City Hall is the most prominent of these. It has splendid frescoes on the outside. I also liked the courtyard of the Old Palace.
This Old Palace now houses the Historical Museum. It has a number of not too interesting exhibitions. Currently, there's also a photo exhibition about WHS in Nepal, Cambodja and Thailand which is worth a look at. I almost had to stay forever in the historical museum as I kept going around in rounds without finding the exit. Fortunately, an employee came to my rescue...