As others have said, the midsized cities are going to be your best bet. Ulm was lovely when I was there, incredibly charming especially in the fall when I was there.

Of course there are many types of German cities, so Ulm will show you something different than, say, Lübeck or Bremen. Southern Germany is what most Americans associate with Germany though, which Ulm can give you.

Milan is a real living breathing city while Florence is a time capsule tourist city. I say this in the best way possible for Florence, I loved the time I spent there. But living there for an extended period time sounds less appealing to me than a vacation. I spent several weeks working in Milan and living the day to day, and found it to be a great place to do exactly that.