places I can recommend, which are not too far: Bamberg and Regensburg. Both are exceptionally beautiful, for all the right reasons! Both are pretty historic cities, both have unique elements (like "little Venice" in Bamberg, or the gorgeous "Dom" in Regensburg" and many, many others) to discover. Both have their own university, so they are buzzing with life, during the day and at night alike. And it is really not far from Würzburg! ;)
RE: Traveling with family. The Würzburg residence