Having spent more than 500 days a tourist in Europe, I put Berlin and Munich near the bottom of places worth visiting-- not as boring as Bern, but close. Amsterdam is only a little better (I've detailed the reasons why tees are not good tourist cities in previous posts, so I'm not going to repeat). The tourist strength of all three is museums, and you say that really isn't your thing.
Interest in Nazis suggests skipping Berlin because the Red Army all but wiped it off the face of the Earth in WWII. There is little of Nazi land left. Templehoff airport is the most interesting, but its status changes daily-- big push a few years ago to tare it down.
Munich has some Nazi history available, especially Dachau in the suburbs.
One day is plenty for Salzburg, so consider a Nazi day trip to Linz, essentially Hitler's home town, and the nearby Mauthausen Death Camp. Hitler & Speer were planning to make Linz the capital of the new Europe. They actually built two of their dream buildings in Linz which are rarely mentioned in guide books, and on the three river cruises we took that stopped at Linz, not one of the 6 guides we had for land tours knew about the Hitler buildings.
How to find Linz' Hitler/Speer buildings: walk down the main drag through the main town square toward the Danube. The two identical buildings separated by the street at the end of tow just before the street drops down to the river bank were built as Hitler's first monuments to his new world order.
On the way to Nuremberg, stop at Regensburg. Do not miss 1) the church opposite the cathedral on the square at the alter end of the cathedral and 2) the hot dog stand at the end of the bridge which has been serving Regensubergerwursts for more that 800 years (we prefer the more refined 600 year old restatement kitty cornered from the hot dog stand under the same management).
More time for the Salzkammergut.