I visited Bamberg in 1997 and second it as a destination. It's in northern Bavaria, probably about 75 miles or so from Weissenburg. Bamberg is small and charming but packs quite a bit of culture. (It used to be called the "untouristy Rothenburg", but I haven't heard it called that in awhile).
Among the sites are a beautiful Residenz (palace); in 1997, tours were available only in German, but maybe that's changed. The cathedral has a couple of interesting elements, including a wood altar carved by Tilman Riemenschneider, who's sometimes called the "German Michelangelo". There's a famed 13th century statue called the Bamberger Reiter, which was the first life-size equestrian stone statue created in Western Europe since classical antiquity. And the only pope buried north of the Alps is in there.
There's a superb Franconian Brewery Museum is housed on the site of monastery. It includes a bar in a beer garden setting: The beer I had was as fine as champagne.
There's interesting literary history in Bamberg. It houses one of the residences of ETA Hoffman, the 18th-19th century writer who in the early 1800s penned The Nutcracker, which became famous half a century later as a ballet. Across the square is a performance venue where Hoffman's musical pieces are occasionally performed. He was a composer, in addition to a writer, and even drew a bit.
Near Bamberg is some interesting World War II-related history. The properties of Von Stauffenberg family -- Greifenstein Castle and Seehof Palace -- are reportedly open to the public. Claus von Stauffenberg is famous for organizing the almost-successful assassination of Hitler.
Aside from all the sites, Bamberg is a charming town traversed by several rivers. You could rent a bicycle. It has great eateries.
