+1... I cant recommend Bamberg highly enough!!
Been there twice and absolutely love the place, honestly one of the nicest places I've ever been! Plus it (and its surrounding area) has the highest number of breweries per capita in the world. The city itself has 8 or 9 all pretty much within walking distance! Its also home to Schlenkerla (the famous Rauchbier). There's something timeless about the place, and drinking smoked beer directly from wooden casks is pretty special (Did I mention its €2.50 per pint!). Theres also some lovely bier Kellers with great views of the whole city as you drink your beer. Its a bit of a trek from Memmingen, but if your making your way to Berlin, its sorta on the way, and a short train from Nuremberg (about 1 hour if I remember correctly).
Its a world heritage center also so the historic center of the City has retained alot of its old charm, and there's surprisingly alot to see/do there.
Highly recommended!