I spent some time in Heidelberg this summer and was disappointed to see how touristy it's become. I lived there in the 60's, and have been back a couple of times but was really struck this time by how much it's changed.

I'd go to Bamberg. It's wonderful!

I just returned from a trip to Bonn, Cologne, Salzburg, and Vienna. I loved Salzburg! I was there for one full day plus my evening of arrival and morning of leaving. If I would have had another day, I could have gone on a lake and mountain bus tour on the second day. They take about 4 hours. It's a very charming and doable city. I loved the views from the fortress, but absolutely enjoyed walking along Monschberg on the high path. (Take a left when leaving the fortress instead of a right to get back to town.) There is a cafe with awesome views on the hike (Stadlm Cafe). Enjoy the beer at Augustiner Braustubl. (I think that's the name of the monk-run brewery a few minutes walk from town.)

Another vote for a Bamberg daytrip from Nberg or a day in Salzburg.

Salzburg is a great city and the Alps are beautiful, but it would take you in the opposite direction from the other cities you plan to see.
I agree more time in Nuremburg with day trips out would make sense. Several people have suggested Bamberg, which is a great suggesetion. Regensburg,Wurzburg and Eichstatt are other personal favorites