Directly in Nuremberg, downtown is very nice. If you're into art and museums, don't miss the Duerer house, and if you're *really* into museums, the Germanisches Nationalmuseum is the place to go. To quote from their www-page: "Its incomparable stores of exceptional art and artisanship afford a panoramic overview of the cultural history of German-speaking central Europe" (starting in 3000 BC...). The presentation is very good (you can spend a whole day in there, but the highlights are presented in a way that 1-2 hours would be enough).

In terms of newer, and much sadder, German history, there is a new documentation center at the Reichsparteitagsgelaende. This was the central grounds where the Nazis held their Germany-wide meetings. The presentation there gives a good overview of this part of German history, which should and will never be forgotten. This can be well combined with the exhibit at the site of the Nuremberg trials (I haven't been there yet but I hear it is very good).

Although I am biased because I live there, may I suggest a day trip to Bamberg? That's about 45 minutes by train/S-bahn (take a day ticket, less than 15 Euros for two people, valid on all public transportation to and in Bamberg [except the ICE]). This is the largest medieval downtown in Germany, much much larger than, e.g., Rothenburg. It's an UNESCO world heritage site and really very, very beautiful. And if you want more than just culture and things like that, it is also the world center of beer brewing (and I'm sure the author of that page will soon also chime in, he knows Franconia better than I'll ever know it, and I live there...). There are lots of good restaurants all over downtown Bamberg.